Calculus & Its Applications (14th Edition)
14th Edition
ISBN: 9780134437774
Author: Larry J. Goldstein, David C. Lay, David I. Schneider, Nakhle H. Asmar
Publisher: PEARSON
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Chapter 6.5, Problem 1E
Determine the average value of
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Trolley of the overhead crane moves along the bridge rail. The trolley position is
measured from the center of the bridge rail (x = 0) is given by x(t) = 0.5t^3-6t^2+19.5t-14 : 0 <= t <= 3 min. The
trolley moves from point A to B in the forward direction, B to C in the reverse direction and C to D again in the
forward direction.
CONTROL PANEL
END TRUCK-
RUNWAY BEAM-
BRIDGE RAIL
HOIST
-TROLLEY
TROLLEY BUMPER
TROLLEY DRIVE
LPENDANT TRACK
-TROLLEY CONDUCTOR
TRACK
WIRE ROPE
-HOOK BLOCK
-BRIDGE DRIVE
-END TRUCK BUMPER
-RUNWAY RAIL
TROLLEY END STOP
-CONDUCTOR BAR
PENDANT FESTOONING
TROLLEY FESTOONING
PENDANT CABLE
PENDANT
x(t)=0.5t^3-6t^2+19.5t-14
v(t)=1.5t^2-12t+19.5
a(t)=(dv(t))/dt=3t-12
Fig. T2.2: The overhead crane
Total masses of the trolley, hook block, and the load attached to the hook block are 110 kg, 20
kg, and 150 kg. Damping coefficient, D, is 40 kg/s.
What is the total amount of energy required from the trolley motor to move the system
[Hint: Use Newton's 2nd law to obtain the…
CONTROL PANEL-
BRIDGE RAIL
HOIST
-TROLLEY
TROLLEY BUMPER
-BRIDGE DRIVE
END TRUCK-
RUNWAY BEAM-
END TRUCK BUMPER
-RUNWAY RAIL
TROLLEY DRIVE
TROLLEY END STOP
-CONDUCTOR BAR
LPENDANT TRACK
TROLLEY CONDUCTOR
TRACK
-WIRE ROPE
PENDANT FESTOONING
TROLLEY FESTOONING
-PENDANT CABLE
-HOOK BLOCK
PENDANT
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Chapter 6 Solutions
Calculus & Its Applications (14th Edition)
Ch. 6.1 - Determine the following: a. t7/2dt b....Ch. 6.1 - Find a function f(t) that satisfies f(t)=3t+5 and...Ch. 6.1 - Find all antiderivatives of each following...Ch. 6.1 - Find all antiderivatives of each following...Ch. 6.1 - Find all antiderivatives of each following...Ch. 6.1 - Find all antiderivatives of each following...Ch. 6.1 - Find all antiderivatives of each following...Ch. 6.1 - Find all antiderivatives of each following...Ch. 6.1 - Determine the following: 4x3dxCh. 6.1 - Determine the following: 13xdx
Ch. 6.1 - Determine the following: 7dxCh. 6.1 - Determine the following: k2dx ((kisaconstant).Ch. 6.1 - Determine the following: xcdx(cisaconstant0)...Ch. 6.1 - Determine the following: xx2dx.Ch. 6.1 - Determine the following: (2x+x2)dx.Ch. 6.1 - Determine the following: 17xdx.Ch. 6.1 - Determine the following: xxdx.Ch. 6.1 - Determine the following: (2x+2x)dx.Ch. 6.1 - Determine the following: (x2x2+13x)dx.Ch. 6.1 - Determine the following: (72x3x3)dx.Ch. 6.1 - Determine the following: 3e2xdx.Ch. 6.1 - Determine the following: exdx.Ch. 6.1 - Determine the following: edx.Ch. 6.1 - Determine the following: 72e2xdx.Ch. 6.1 - Determine the following: 2(e2x+1)dx.Ch. 6.1 - Determine the following: (3ex+2xe0.5x2)dx.Ch. 6.1 - In Exercises 25-36, find the value of k that makes...Ch. 6.1 - In Exercises 25-36, find the value of k that makes...Ch. 6.1 - In Exercises 25-36, find the value of k that makes...Ch. 6.1 - In Exercises 25-36, find the value of k that makes...Ch. 6.1 - In Exercises 25-36, find the value of k that makes...Ch. 6.1 - In Exercises 25-36, find the value of k that makes...Ch. 6.1 - In Exercises 25-36, find the value of k that makes...Ch. 6.1 - In Exercises 25-36, find the value of k that makes...Ch. 6.1 - In Exercises 25-36, find the value of k that makes...Ch. 6.1 - In Exercises 25-36, find the value of k that makes...Ch. 6.1 - In Exercises 25-36, find the value of k that makes...Ch. 6.1 - In Exercises 25-36, find the value of k that makes...Ch. 6.1 - Find all functions f(t) that satisfy the given...Ch. 6.1 - Find all functions f(t) that satisfy the given...Ch. 6.1 - Find all functions f(t) that satisfy the given...Ch. 6.1 - Find all functions f(t) that satisfy the given...Ch. 6.1 - Find all functions f(x) that satisfy the given...Ch. 6.1 - Find all functions f(x) that satisfy the given...Ch. 6.1 - Find all functions f(x) that satisfy the given...Ch. 6.1 - Find all functions f(x) that satisfy the given...Ch. 6.1 - Find all functions f(x) that satisfy the given...Ch. 6.1 - Find all functions f(x) that satisfy the given...Ch. 6.1 - Figure 4 shows the graphs of several functions...Ch. 6.1 - Figure 5 shows the graphs of several functions...Ch. 6.1 - Which of the following is lnxdx ? a.1x+C b.xlnxx+C...Ch. 6.1 - Which of the following is xx+1dx?...Ch. 6.1 - Figure 6 contains the graph of a function F(x). On...Ch. 6.1 - Figure 7 contains an antiderivative of the...Ch. 6.1 - The function g(x) in Fig. 8, resulted from...Ch. 6.1 - The function g(x) in Fig.9 resulted from shifting...Ch. 6.1 - Height of a Ball A ball is thrown upward from a...Ch. 6.1 - Free Fall A rock is dropped from the top of a...Ch. 6.1 - Rate of Production Let P(t) be the total output of...Ch. 6.1 - Rate of Production After t hours of operation, a...Ch. 6.1 - Heat DiffusionA package of frozen strawberries is...Ch. 6.1 - Epidemic A flu epidemic hits a town. Let P(t) be...Ch. 6.1 - Profit A small tie shop finds that at a sales...Ch. 6.1 - Prob. 62ECh. 6.1 - Prob. 63ECh. 6.1 - U.S. Natural Gas Production Since 1987, the rate...Ch. 6.1 - Prob. 65ECh. 6.1 - Prob. 66ECh. 6.1 - Prob. 67ECh. 6.1 - Prob. 68ECh. 6.2 - Evaluate 01e2x1exdx.Ch. 6.2 - If f(t)=1t, find f(2)f(0).Ch. 6.2 - In Exercises 114, evaluate the given integral....Ch. 6.2 - In Exercises 114, evaluate the given integral....Ch. 6.2 - In Exercises 114, evaluate the given integral....Ch. 6.2 - In Exercises 114, evaluate the given integral....Ch. 6.2 - In Exercises 114, evaluate the given integral....Ch. 6.2 - In Exercises 114, evaluate the given integral....Ch. 6.2 - In Exercises 114, evaluate the given integral....Ch. 6.2 - In Exercises 114, evaluate the given integral....Ch. 6.2 - In Exercises 114, evaluate the given integral....Ch. 6.2 - In Exercises 114, evaluate the given integral....Ch. 6.2 - In Exercises 114, evaluate the given integral....Ch. 6.2 - In Exercises 114, evaluate the given integral....Ch. 6.2 - In Exercises 114, evaluate the given integral....Ch. 6.2 - In Exercises 114, evaluate the given integral....Ch. 6.2 - Given 01f(x)dx=3.5 and 14f(x)dx=5, find 04f(x)dx.Ch. 6.2 - Given 11f(x)dx=0 and 110f(x)dx=4, find 110f(x)dx.Ch. 6.2 - Given 13f(x)dx=3 and 13g(x)dx=1, find...Ch. 6.2 - Given 0.53f(x)dx=0 and 0.53(2g(x)+f(x))dx=4, find...Ch. 6.2 - In Exercises 1922, combine the integrals into one...Ch. 6.2 - In Exercises 1922, combine the integrals into one...Ch. 6.2 - In Exercises 1922, combine the integrals into one...Ch. 6.2 - In Exercises 1922, combine the integrals into one...Ch. 6.2 - In Exercises 2326, use formula (8) to help you...Ch. 6.2 - In Exercises 2326, use formula (8) to help you...Ch. 6.2 - In Exercises 2326, use formula (8) to help you...Ch. 6.2 - In Exercises 2326, use formula (8) to help you...Ch. 6.2 - Refer to Fig. 4 and evaluate 02f(x)dx. Figure 4Ch. 6.2 - Refer to Fig. 5 and evaluate 03f(x)dx. Figure 5Ch. 6.2 - Refer to Fig. 6 and evaluate 11f(t)dt. Figure 6Ch. 6.2 - Refer to Fig. 7 and evaluate 12f(t)dt. Figure 7Ch. 6.2 - Net Change in Position A rock is dropped from the...Ch. 6.2 - Net change in Position The velocity at time t...Ch. 6.2 - Net Change in Position The velocity at time t...Ch. 6.2 - Velocity of a Skydiver The velocity of a skydiver...Ch. 6.2 - Net Change in Cost A companys marginal cost...Ch. 6.2 - Prob. 36ECh. 6.2 - Net Increase of an Investment An investment grew...Ch. 6.2 - Depreciation of Real Estate A property with an...Ch. 6.2 - Population Model with Emigration The rate of...Ch. 6.2 - Paying Down a Mortgage You took a 200,000 home...Ch. 6.2 - Mortgage Using the data from the previous...Ch. 6.2 - Radioactive Decay A sample of radioactive material...Ch. 6.2 - Prob. 43ECh. 6.2 - Level of Water in a Tank A conical-shaped tank is...Ch. 6.3 - Repeat Example 6 using midpoints of the...Ch. 6.3 - Repeat Example 6 using left endpoints of the...Ch. 6.3 - In exercises 16, compute the area of the shaded...Ch. 6.3 - In exercises 16, compute the area of the shaded...Ch. 6.3 - In exercise 16, compute the area of the shaded...Ch. 6.3 - In exercise 16, compute the area of the shaded...Ch. 6.3 - In exercise 16, compute the area of the shaded...Ch. 6.3 - In exercise 16, compute the area of the shaded...Ch. 6.3 - In exercises 712, set-up the definite integral...Ch. 6.3 - In exercises 712, set-up the definite integral...Ch. 6.3 - In exercises 712, set-up the definite integral...Ch. 6.3 - In exercises 712, set-up the definite integral...Ch. 6.3 - In exercises 712, set-up the definite integral...Ch. 6.3 - Prob. 12ECh. 6.3 - Prob. 13ECh. 6.3 - Prob. 14ECh. 6.3 - Prob. 15ECh. 6.3 - In Exercises 1618, draw the region whose area is...Ch. 6.3 - In Exercises 1618, draw the region whose area is...Ch. 6.3 - In Exercises 1618, draw the region whose area is...Ch. 6.3 - Find the area under each of the given curves....Ch. 6.3 - Find the area under each of the given curves....Ch. 6.3 - Find the area under each of the given curves....Ch. 6.3 - Find the area under each of the given curves....Ch. 6.3 - Find the area under each of the given curves....Ch. 6.3 - Find the area under each of the given curves....Ch. 6.3 - Prob. 25ECh. 6.3 - Find the real number b0 so that the area under the...Ch. 6.3 - Determine x and the midpoints of the subintervals...Ch. 6.3 - Determine x and the midpoints of the subintervals...Ch. 6.3 - Determine x and the midpoints of the subintervals...Ch. 6.3 - Determine x and the midpoints of the subintervals...Ch. 6.3 - In Exercises 3136, use a Riemann sum to...Ch. 6.3 - In Exercises 3136, use a Riemann sum to...Ch. 6.3 - In Exercises 3136, use a Riemann sum to...Ch. 6.3 - In Exercises 3136, use a Riemann sum to...Ch. 6.3 - In Exercises 3136, use a Riemann sum to...Ch. 6.3 - In Exercises 3136, use a Riemann sum to...Ch. 6.3 - In Exercises 3740, use a Riemann sum to...Ch. 6.3 - In Exercises 3740, use a Riemann sum to...Ch. 6.3 - In Exercises 3740, use a Riemann sum to...Ch. 6.3 - Prob. 40ECh. 6.3 - Use a Riemann sum with n=4 and left endpoints to...Ch. 6.3 - Prob. 42ECh. 6.3 - The graph of the function f(x)=1x2 on the interval...Ch. 6.3 - Use a Riemann sum with n=5 and midpoints to...Ch. 6.3 - Estimate the area (in square feet) of the...Ch. 6.3 - Prob. 46ECh. 6.3 - Prob. 47ECh. 6.3 - Prob. 48ECh. 6.3 - Technology Exercises. The area under the graph of...Ch. 6.3 - Prob. 50ECh. 6.3 - Prob. 51ECh. 6.3 - Prob. 52ECh. 6.4 - Find the area between the curves y=x+3 and...Ch. 6.4 - A company plans to increase its production from 10...Ch. 6.4 - Write a definite integral or sum of definite...Ch. 6.4 - Write a definite integral or sum of definite...Ch. 6.4 - Shade the portion of Fig. 23 whose area is given...Ch. 6.4 - Shade the portion ofFig. 24 whose area is given by...Ch. 6.4 - Let f(x) be the function pictured in Fig. 25....Ch. 6.4 - Let g(x) be the function pictured in Fig. 26....Ch. 6.4 - Find the area of the region between the curve and...Ch. 6.4 - Find the area of the region between the curve and...Ch. 6.4 - Find the area of the region between the curve and...Ch. 6.4 - Find the area of the region between the curve and...Ch. 6.4 - Find the area of the region between the curve and...Ch. 6.4 - Find the area of the region between the curve and...Ch. 6.4 - Find the area of the region between the curves....Ch. 6.4 - Find the area of the region between the curves....Ch. 6.4 - Find the area of the region between the curves....Ch. 6.4 - Find the area of the region between the curves....Ch. 6.4 - Find the area of the region between the curves....Ch. 6.4 - Find the area of the region between the curves....Ch. 6.4 - Find the area of the region bounded by the curves....Ch. 6.4 - Find the area of the region bounded by the curves....Ch. 6.4 - Find the area of the region bounded by the curves....Ch. 6.4 - Find the area of the region bounded by the curves....Ch. 6.4 - Find the area of the region bounded by the curves....Ch. 6.4 - Find the area of the region bounded by the curves....Ch. 6.4 - Find the area of the region bounded by the curves....Ch. 6.4 - Find the area of the region bounded by the curves....Ch. 6.4 - Find the area of the region between y=x23x and the...Ch. 6.4 - Find the area of the region between y=x2 and...Ch. 6.4 - Find the area in Fig. 27 of the region bounded by...Ch. 6.4 - Find the area of the region bounded by y=1/x,y=4x...Ch. 6.4 - Height of a Helicopter A helicopter is rising...Ch. 6.4 - Assembly line productionAfter t hour of operation,...Ch. 6.4 - Cost Suppose that the marginal cost function for a...Ch. 6.4 - ProfitSuppose that the marginal profit function...Ch. 6.4 - Marginal Profit Let M(x) be a companys marginal...Ch. 6.4 - Marginal Profit Let M(x) be a companys marginal...Ch. 6.4 - Prob. 37ECh. 6.4 - VelocitySuppose that the velocity of a car at time...Ch. 6.4 - Deforestation and Fuel wood Deforestation is one...Ch. 6.4 - Refer to Exercise 39. The rate of new tree growth...Ch. 6.4 - After an advertising campaign, a companys marginal...Ch. 6.4 - Profit and Area The marginal profit for a certain...Ch. 6.4 - Velocity and Distance Two rockets are fired...Ch. 6.4 - Distance TraveledCars A and B start at the same...Ch. 6.4 - Displacement versus Distance Traveled The velocity...Ch. 6.4 - Displacement versus Distance Traveled The velocity...Ch. 6.4 - Prob. 47ECh. 6.4 - Prob. 48ECh. 6.4 - Prob. 49ECh. 6.4 - Prob. 50ECh. 6.5 - A rock dropped from a bridge has a velocity of 32t...Ch. 6.5 - An Investment yields a continuous income stream of...Ch. 6.5 - Determine the average value of f(x) over the...Ch. 6.5 - Determine the average value of f(x) over the...Ch. 6.5 - Determine the average value of f(x) over the...Ch. 6.5 - Prob. 4ECh. 6.5 - Determine the average value of f(x) over the...Ch. 6.5 - Prob. 6ECh. 6.5 - Average Temperature During a certain 12-hour...Ch. 6.5 - Average PopulationAssuming that a countrys...Ch. 6.5 - Average Amount of Radium. One hundred grams of...Ch. 6.5 - Average Amount of Money. One hundred dollars is...Ch. 6.5 - Consumers Surplus Find the consumers surplus for...Ch. 6.5 - Consumers Surplus Find the consumers surplus for...Ch. 6.5 - Consumers Surplus Find the consumers surplus for...Ch. 6.5 - Consumers Surplus Find the consumers surplus for...Ch. 6.5 - Prob. 15ECh. 6.5 - Prob. 16ECh. 6.5 - Prob. 17ECh. 6.5 - Prob. 18ECh. 6.5 - Prob. 19ECh. 6.5 - Prob. 20ECh. 6.5 - Prob. 21ECh. 6.5 - Prob. 22ECh. 6.5 - Prob. 23ECh. 6.5 - Future Value Suppose that money is deposited...Ch. 6.5 - Prob. 25ECh. 6.5 - Prob. 26ECh. 6.5 - Volume of Solids of Revolution Find the volume of...Ch. 6.5 - Volume of Solids of Revolution Find the volume of...Ch. 6.5 - Prob. 29ECh. 6.5 - Prob. 30ECh. 6.5 - Prob. 31ECh. 6.5 - Prob. 32ECh. 6.5 - Prob. 33ECh. 6.5 - Prob. 34ECh. 6.5 - Prob. 35ECh. 6.5 - Prob. 36ECh. 6.5 - Prob. 37ECh. 6.5 - For the Riemann sum...Ch. 6.5 - Prob. 39ECh. 6.5 - Prob. 40ECh. 6.5 - Prob. 41ECh. 6.5 - Prob. 42ECh. 6.5 - Prob. 43ECh. 6.5 - Prob. 44ECh. 6.5 - Prob. 45ECh. 6.5 - Prob. 46ECh. 6 - What does it mean to antidifferentiate a function?Ch. 6 - Prob. 2CCECh. 6 - Prob. 3CCECh. 6 - Prob. 4CCECh. 6 - Prob. 5CCECh. 6 - Prob. 6CCECh. 6 - Prob. 7CCECh. 6 - Prob. 8CCECh. 6 - Prob. 9CCECh. 6 - Prob. 10CCECh. 6 - Prob. 11CCECh. 6 - Calculate the following integrals. 32dxCh. 6 - Prob. 2RECh. 6 - Calculate the following integrals. x+1dxCh. 6 - Calculate the following integrals. 2x+4dxCh. 6 - Calculate the following integrals. 2(x3+3x21)dxCh. 6 - Calculate the following integrals. x+35dxCh. 6 - Calculate the following integrals. ex/2dxCh. 6 - Calculate the following integrals. 5x7dxCh. 6 - Calculate the following integrals. (3x44x3)dxCh. 6 - Calculate the following integrals. (2x+3)7dxCh. 6 - Calculate the following integrals. 4xdxCh. 6 - Calculate the following integrals. (5xx5)dxCh. 6 - Calculate the following integrals. 11(x+1)2dxCh. 6 - Calculate the following integrals. 01/8x3dxCh. 6 - Calculate the following integrals. 122x+4dxCh. 6 - Calculate the following integrals. 201(2x+11x+4)dxCh. 6 - Calculate the following integrals. 124x5dxCh. 6 - Calculate the following integrals. 2308x+1dxCh. 6 - Calculate the following integrals. 141x2dxCh. 6 - Calculate the following integrals. 36e2(x/3)dxCh. 6 - Calculate the following integrals. 05(5+3x)1dxCh. 6 - Calculate the following integrals. 2232e3xdxCh. 6 - Calculate the following integrals. 0ln2(exex)dxCh. 6 - Calculate the following integrals. ln2ln3(ex+ex)dxCh. 6 - Calculate the following integrals. 0ln3ex+exe2xdxCh. 6 - Calculate the following integrals. 013+e2xexdxCh. 6 - Find the area under the curve y=(3x2)3 from x=1 to...Ch. 6 - Find the area under the curve y=1+x from x=1 to...Ch. 6 - In Exercises 2936, Find the area of the shaded...Ch. 6 - In Exercises 2936, Find the area of the shaded...Ch. 6 - In Exercises 2936, Find the area of the shaded...Ch. 6 - In Exercises 2936, Find the area of the shaded...Ch. 6 - In Exercises 2936, Find the area of the shaded...Ch. 6 - In Exercises 2936, Find the area of the shaded...Ch. 6 - In Exercises 2936, Find the area of the shaded...Ch. 6 - In Exercises 2936, Find the area of the shaded...Ch. 6 - Find the area of the region bounded by the curves...Ch. 6 - Find the area of the region between the curves...Ch. 6 - Find the function f(x) for which...Ch. 6 - Find the function f(x) for which f(x)=e5x,f(0)=1.Ch. 6 - Describe all solutions of the following...Ch. 6 - Let k be a constant, and let y=f(t) be a function...Ch. 6 - Prob. 43RECh. 6 - Prob. 44RECh. 6 - A drug is injected into a patient at the rate of...Ch. 6 - A rock thrown straight up into the air has a...Ch. 6 - Prob. 47RECh. 6 - Prob. 48RECh. 6 - Prob. 49RECh. 6 - Prob. 50RECh. 6 - Find the consumers surplus for the demand curve...Ch. 6 - Three thousand dollars is deposited in the bank at...Ch. 6 - Find the average value of f(x)=1/x3 from x=13 to...Ch. 6 - Prob. 54RECh. 6 - In Fig. 2, three regions are labelled with their...Ch. 6 - Prob. 56RECh. 6 - Prob. 57RECh. 6 - Prob. 58RECh. 6 - Prob. 59RECh. 6 - Prob. 60RECh. 6 - Prob. 61RECh. 6 - Prob. 62RECh. 6 - Prob. 63RECh. 6 - Prob. 64RECh. 6 - Prob. 65RECh. 6 - Prob. 66RECh. 6 - Prob. 67RECh. 6 - Prob. 68RECh. 6 - Prob. 69RECh. 6 - Prob. 70RECh. 6 - Prob. 71RECh. 6 - Prob. 72RECh. 6 - Prob. 73RECh. 6 - Prob. 74RE
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- Please sketch questions 1, 2 and 6arrow_forwardsolve questions 3, 4,5, 7, 8, and 9arrow_forward4. Please solve this for me and show every single step. I am studying and got stuck on this practice question, and need help in solving it. Please be very specific and show every step. Thanks. I WANT A HUMAN TO SOLVE THIS PLEASE.arrow_forward
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- 1. Please solve this for me and show every single step. I am studying and got stuck on this practice question, and need help in solving it. Please be very specific and show every step. Thanks.arrow_forwardQ1/Details of square footing are as follows: DL = 800 KN, LL = 500 kN, Fy=414 MPa, Fc = 20 MPa Footing, qa = 120 kPa, Column (400x400) mm. Determine the dimensions of footing and thickness? Q2/ For the footing system shown in Figure below, find the suitable size (BxL) for: 1. Non uniform pressure, 2. Uniform pressure, 3.Uniform pressure with moment in clockwise direction. (Use qmax=qall =200kPa). Property, line M=200KN.m 1m P-1000KNarrow_forwardQ2/ Determine the size of square footing to carry net allowable load of 400 kN. FS-3. Use Terzaghi equation assuming general shear failure. 400KN 1 m += 35" C=0.0 Ya = 18.15 kN/m³ +=25" C=50 kN/m² Ya 20 kN/m³arrow_forward
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Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Definite Integral Calculus Examples, Integration - Basic Introduction, Practice Problems; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=rCWOdfQ3cwQ;License: Standard YouTube License, CC-BY