
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Question
Chapter 8, Problem 8RE
To determine
To find: The area of the surface obtained by rotating the sine curve about x-axis using Simpson’s rule.
Expert Solution & Answer

Trending nowThis is a popular solution!

Students have asked these similar questions
2. Find the Bezier surface equation using the 9 control points shown below. Use
the u and v directions shown. It is required to show all the calculation processes
for finding Bernstein polynomials. Find the surface tangent, twist and normal
vectors at point u=0.5 and v=0.5. (40 points)
y
10
9
8
7
6
5
4
3
2
Poo
и
1
1 2 3 4 5 6 7 8 9
10
10
X
A cable runs along the wall from C to P at a cost
of $24 per meter, and straight from P to M at a
cost of $26 per meter. If M is 10 meters from the
nearest point A on the wall where P lies, and A is
72 meters from C, find the distance from C to P
such that the cost of installing the cable is
minimized and find this cost.
C
72
P
A
10
M
The number of bank robberies in a country for the years 2010-2018 is given in the following figure. Consider the
closed interval [2010,2018].
(a) Give all relative maxima and minima and when they occur on the interval.
(b) Give the absolute maxima and minima and when they occur on the interval.
Incidents
7000-
6000-5
5482
5000-
4424
4273
4822
4000-
3708
3748
4229
4089
3000-
2582
2000-
1000-
0
2010
2012
2014
2016
2018
Year
Chapter 8 Solutions
Calculus: Early Transcendentals
Ch. 8.1 - Use the arc length formula (3) to find the length...Ch. 8.1 - Use the arc length formula to find the length of...Ch. 8.1 - Set up an integral that represents the length of...Ch. 8.1 - Set up an integral that represents the length of...Ch. 8.1 - Set up an integral that represents the length of...Ch. 8.1 - Set up an integral that represents the length of...Ch. 8.1 - Set up an integral that represents the length of...Ch. 8.1 - Set up an integral that represents the length of...Ch. 8.1 - Find the exact length of the curve. 9. y = 1 +...Ch. 8.1 - Find the exact length of the curve. 10. 36y2 = (x2...
Ch. 8.1 - Find the exact length of the curve. 11....Ch. 8.1 - Find the exact length of the curve. 12....Ch. 8.1 - Find the exact length of the curve. 13....Ch. 8.1 - Find the exact length of the curve. 14. y = ln(cos...Ch. 8.1 - Find the exact length of the curve. 15. y = ln(sec...Ch. 8.1 - Find the exact length of the curve. 16....Ch. 8.1 - Find the exact length of the curve. 17....Ch. 8.1 - Find the exact length of the curve. 18....Ch. 8.1 - Find the exact length of the curve. 19....Ch. 8.1 - Find the exact length of the curve. 20. y = 1 ex,...Ch. 8.1 - Find the length of the arc of the curve from point...Ch. 8.1 - Find the length of the arc of the curve from point...Ch. 8.1 - Graph the curve and visually estimate its length....Ch. 8.1 - Graph the curve and visually estimate its length....Ch. 8.1 - Use Simpsons Rule with n = 10 to estimate the arc...Ch. 8.1 - Use Simpsons Rule with n = 10 to estimate the arc...Ch. 8.1 - Use Simpsons Rule with n = 10 to estimate the arc...Ch. 8.1 - Use Simpsons Rule with n = 10 to estimate the arc...Ch. 8.1 - Prob. 29ECh. 8.1 - Prob. 30ECh. 8.1 - Sketch the curve with equation x2/3 + y2/3 = 1 and...Ch. 8.1 - (a) Sketch the curve y3 = x2. (b) Use Formulas 3...Ch. 8.1 - Find the arc length function for the curve y =...Ch. 8.1 - (a) Find the arc length function for the curve y =...Ch. 8.1 - Find the arc length function for the curve...Ch. 8.1 - The arc length function for a curve y = f(x),...Ch. 8.1 - For the function f(x)=14ex+ex, prove that the arc...Ch. 8.1 - A steady wind blows a kite due west. The kites...Ch. 8.1 - A hawk flying at 15m/s at an altitude of 180 m...Ch. 8.1 - The Gateway Arch in St. Louis (see the photo on...Ch. 8.1 - A manufacturer of corrugated metal roofing wants...Ch. 8.1 - (a) The figure shows a telephone wire hanging...Ch. 8.1 - Prob. 45ECh. 8.1 - The curves with equations xn + yn = 1, n = 4, 6,...Ch. 8.2 - (a) Set up an integral for the area of the surface...Ch. 8.2 - (a) Set up an integral for the area of the surface...Ch. 8.2 - (a) Set up an integral for the area of the surface...Ch. 8.2 - (a) Set up an integral for the area of the surface...Ch. 8.2 - (a) Set up an integral for the area of the surface...Ch. 8.2 - (a) Set up an integral for the area of the surface...Ch. 8.2 - Find the exact area of the surface obtained by...Ch. 8.2 - Find the exact area of the surface obtained by...Ch. 8.2 - Find the exact area of the surface obtained by...Ch. 8.2 - Find the exact area of the surface obtained by...Ch. 8.2 - Find the exact area of the surface obtained by...Ch. 8.2 - Find the exact area of the surface obtained by...Ch. 8.2 - Find the exact area of the surface obtained by...Ch. 8.2 - Find the exact area of the surface obtained by...Ch. 8.2 - The given curve is rotated about the y-axis. Find...Ch. 8.2 - The given curve is rotated about the y-axis. Find...Ch. 8.2 - The given curve is rotated about the y-axis. Find...Ch. 8.2 - The given curve is rotated about the y-axis. Find...Ch. 8.2 - Use Simpsons Rule with n = 10 to approximate the...Ch. 8.2 - Use Simpsons Rule with n = 10 to approximate the...Ch. 8.2 - Prob. 21ECh. 8.2 - Use Simpsons Rule with n = 10 to approximate the...Ch. 8.2 - Use either a CAS or a table of integrals to find...Ch. 8.2 - Use either a CAS or a table of integrals to find...Ch. 8.2 - If the region = {(x, y) | x 1, 0 y 1/x} is...Ch. 8.2 - If the infinite curve y = ex, x 0, is rotated...Ch. 8.2 - Prob. 29ECh. 8.2 - A group of engineers is building a parabolic...Ch. 8.2 - (a) The ellipse x2a2+y2b2=1ab is rotated about the...Ch. 8.2 - Find the surface area of the torus in Exercise...Ch. 8.2 - If the curve y = f(x), a x b, is rotated about...Ch. 8.2 - Find the area of the surface obtained by rotating...Ch. 8.2 - (a) Show that the surface area of a zone of a...Ch. 8.2 - Show that if we rotate the curve y = ex/2 + e x/2...Ch. 8.2 - Prob. 38ECh. 8.2 - Formula 4 is valid only when f(x) 0. Show that...Ch. 8.3 - An aquarium 5 ft long, 2 ft wide, and 3 ft deep is...Ch. 8.3 - A tank is 8 m long, 4 m wide, 2 m high, and...Ch. 8.3 - A vertical plate is submerged (or partially...Ch. 8.3 - A vertical plate is submerged (or partially...Ch. 8.3 - A vertical plate is submerged (or partially...Ch. 8.3 - A vertical plate is submerged (or partially...Ch. 8.3 - A vertical plate is submerged (or partially...Ch. 8.3 - A vertical plate is submerged (or partially...Ch. 8.3 - A vertical plate is submerged (or partially...Ch. 8.3 - A vertical plate is submerged (or partially...Ch. 8.3 - A vertical plate is submerged (or partially...Ch. 8.3 - A milk truck carries milk with density 64.6 lb/ft3...Ch. 8.3 - A trough is filled with a liquid of density 840...Ch. 8.3 - A vertical dam has a semicircular gate as shown in...Ch. 8.3 - A cube with 20-cm-long sides is sitting on the...Ch. 8.3 - Prob. 16ECh. 8.3 - A swimming pool is 20 ft wide and 40 ft long and...Ch. 8.3 - Suppose that a plate is immersed vertically in a...Ch. 8.3 - A metal plate was found submerged vertically in...Ch. 8.3 - (a) Use the formula of Exercise 18 to show that...Ch. 8.3 - Point-masses mi arc located on the x-axis as...Ch. 8.3 - Point-masses mi arc located on the x-axis as...Ch. 8.3 - The masses mi, are located at the points Pi. Find...Ch. 8.3 - The masses mi, are located at the points Pi. Find...Ch. 8.3 - Sketch the region bounded by the curves, and...Ch. 8.3 - Sketch the region bounded by the curves, and...Ch. 8.3 - Sketch the region bounded by the curves, and...Ch. 8.3 - Sketch the region bounded by the curves, and...Ch. 8.3 - Find the centroid of the region bounded by the...Ch. 8.3 - Find the centroid of the region bounded by the...Ch. 8.3 - Find the centroid of the region bounded by the...Ch. 8.3 - Find the centroid of the region bounded by the...Ch. 8.3 - Find the centroid of the region bounded by the...Ch. 8.3 - Calculate the moments Mx and My and the center of...Ch. 8.3 - Calculate the moments Mx and My and the center of...Ch. 8.3 - Use Simpsons Rule to estimate the centroid of the...Ch. 8.3 - Find the centroid of the region bounded by the...Ch. 8.3 - Prob. 38ECh. 8.3 - Prove that the centroid of any triangle is located...Ch. 8.3 - Find the centroid of the region shown, not by...Ch. 8.3 - Find the centroid of the region shown, not by...Ch. 8.3 - A rectangle with sides a and b is divided into...Ch. 8.3 - Prob. 43ECh. 8.3 - Use the Theorem of Pappus to find the volume of...Ch. 8.3 - Use the Theorem of Pappus to find the volume of...Ch. 8.3 - Use the Theorem of Pappus to find the volume of...Ch. 8.3 - The centroid of a curve can be found by a process...Ch. 8.3 - The Second Theorem of Pappus is in the same spirit...Ch. 8.3 - Use the Second Theorem of Pappus described in...Ch. 8.3 - Let be the region that lies between the curves...Ch. 8.3 - Prove Formulas 9.Ch. 8.4 - The marginal cost function C(x) was defined to be...Ch. 8.4 - A company estimates that the marginal revenue (in...Ch. 8.4 - Prob. 3ECh. 8.4 - The demand function for a particular vacation...Ch. 8.4 - A demand curve is given by p = 450/(x + 8). Find...Ch. 8.4 - The supply function ps(x) for a commodity gives...Ch. 8.4 - If a supply curve is modeled by the equation p =...Ch. 8.4 - In a purely competitive market, the price of a...Ch. 8.4 - The sum of consumer surplus and producer surplus...Ch. 8.4 - A camera company estimates that the demand...Ch. 8.4 - A company modeled the demand curve for its product...Ch. 8.4 - A movie theater has been charging 10.00 per...Ch. 8.4 - Prob. 13ECh. 8.4 - Prob. 14ECh. 8.4 - Prob. 15ECh. 8.4 - Prob. 16ECh. 8.4 - Prob. 17ECh. 8.4 - Prob. 18ECh. 8.4 - Use Poiseuilles Law to calculate the rate of flow...Ch. 8.4 - Prob. 20ECh. 8.4 - The dye dilution method is used to measure cardiac...Ch. 8.4 - After a 5.5-mg injection of dye, the readings of...Ch. 8.4 - The graph of the concentration function c(t) is...Ch. 8.5 - Let f(x) be the probability density function for...Ch. 8.5 - Let f(t) be the probability density function for...Ch. 8.5 - Let .f(x) = 30x2(1 x)2 for 0 x 1 and f(x) = 0...Ch. 8.5 - The density function f(x)=e3x(1+e3x)2 is an...Ch. 8.5 - Let f(x) = c/(1 + x2). (a) For what value of c is...Ch. 8.5 - Let f(x) = k(3x x2) if 0 x 3 and f(x) = 0 if x ...Ch. 8.5 - A spinner from a board game randomly indicates a...Ch. 8.5 - (a) Explain why the function whose graph is shown...Ch. 8.5 - Show that the median waiting time for a phone call...Ch. 8.5 - (a) A type of light bulb is labeled as having an...Ch. 8.5 - An online retailer has determined that the average...Ch. 8.5 - Prob. 12ECh. 8.5 - REM sleep is the phase of sleep when most active...Ch. 8.5 - According to the National Health Survey, the...Ch. 8.5 - The Garbage Project at the University of Arizona...Ch. 8.5 - Boxes are labeled as containing 500 g of cereal....Ch. 8.5 - The speeds of vehicles on a highway with speed...Ch. 8.5 - Prob. 18ECh. 8.5 - Prob. 19ECh. 8.5 - Prob. 20ECh. 8.5 - The hydrogen atom is composed of one proton in the...Ch. 8 - (a) How is the length of a curve defined? (b)...Ch. 8 - Prob. 2RCCCh. 8 - Describe how we can find the hydrostatic force...Ch. 8 - Prob. 4RCCCh. 8 - Prob. 5RCCCh. 8 - Prob. 6RCCCh. 8 - Prob. 7RCCCh. 8 - Prob. 8RCCCh. 8 - Prob. 9RCCCh. 8 - Prob. 10RCCCh. 8 - Find the length of the curve. y = 4(x 1)3/2, 1 x...Ch. 8 - Find the length of the curve. y=2ln(sin12x),/3xCh. 8 - Find the length of the curve. 12x = 4y3 + 3y1, 1 ...Ch. 8 - (a) Find the length of the curve y=x416+12x21x2...Ch. 8 - Prob. 5RECh. 8 - (a) The curve y = x2, 0 x 1, is rotated about...Ch. 8 - Use Simpson's Rule with n = 10 to estimate the...Ch. 8 - Prob. 8RECh. 8 - Find the length of the curve y=1xt1dt1x16Ch. 8 - Prob. 10RECh. 8 - A gate in an irrigation canal is constructed in...Ch. 8 - A trough is filled with water and its vertical...Ch. 8 - Find the centroid of the region shown.Ch. 8 - Find the centroid of the region shown.Ch. 8 - Find the centroid of the region bounded by the...Ch. 8 - Find the centroid of the region bounded by the...Ch. 8 - Prob. 17RECh. 8 - Use the Theorem of Pappus and the fact that the...Ch. 8 - The demand function for a commodity is given by p...Ch. 8 - After a 6-mg injection of dye into a heart, the...Ch. 8 - Prob. 21RECh. 8 - Prob. 22RECh. 8 - Prob. 23RECh. 8 - Prob. 1PCh. 8 - Find the centroid of the region enclosed by the...Ch. 8 - If a sphere of radius r is sliced by a plane whose...Ch. 8 - Prob. 4PCh. 8 - Prob. 5PCh. 8 - The figure shows a semicircle with radius 1,...Ch. 8 - Prob. 7PCh. 8 - Consider a flat metal plate to be placed...Ch. 8 - A uniform disk with radius 1 m is to be cut by a...Ch. 8 - A triangle with area 30 cm2 is cut from a corner...Ch. 8 - Prob. 11PCh. 8 - If the needle in Problem 11 has length h L, its...Ch. 8 - Find the centroid of the region enclosed by the...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.Similar questions
- please do 8.1 q7arrow_forwardplease do 8.1 q6arrow_forwardIf the price charged for a candy bar is p(x) cents, then x thousand candy bars will be sold in a certain city, where p(x)=158- X 10° a. Find an expression for the total revenue from the sale of x thousand candy bars. b. Find the value of x that leads to maximum revenue. c. Find the maximum revenue.arrow_forward
- 3 The total profit P(X) (in thousands of dollars) from the sale of x hundred thousand automobile tires is approximated by P(x) = -x³ + 12x² + 60x - 200, x≥5. Find the number of hundred thousands of tires that must be sold to maximize profit. Find the maximum profit. The maximum profit is $ when hundred thousand tires are sold.arrow_forwardA fence must be built to enclose a rectangular area of 5000 ft². Fencing material costs $4 per foot for the two sides facing north and south and $8 per foot for the other two sides. Find the cost of the least expensive fence. The cost of the least expensive fence is $ (Simplify your answer.)arrow_forwardThe number of fish swimming upstream to spawn is approximated by the function given below, where x represents the temperature of the water in degrees Celsius. Find the water temperature that produces the maximum number of fish swimming upstream. F(x) = x3 + 3x² + 360x + 5017, 5≤x≤18arrow_forward
- A campground owner has 500 m of fencing. He wants to enclose a rectangular field bordering a river, with no fencing along the river. (See the sketch.) Let x represent the width of the field. (a) Write an expression for the length of the field as a function of x. (b) Find the area of the field (area = length x width) as a function of x. (c) Find the value of x leading to the maximum area. (d) Find the maximum area. x Riverarrow_forwardA rectangular tank with a square base, an open top, and a volume of 1372 ft³ is to be constructed of sheet steel. Find the dimensions of the tank that has the minimum surface area. The dimensions of the tank with minimum surface area are (Simplify your answer. Use a comma to separate answers.) ft.arrow_forwardWrite an equation for the function graphed below 5+ 4 - -7 -6 -5 -4 -3 -2 -1 y = 3. 2 1 + 1 2 3 4 5 6 7 -1 -3 -4 5 -5+ aarrow_forward
- Approximate graphically the radius and height of a cylindrical container with volume 50 cubic inches and lateral surface area 75 square inches. h 2лr The radius is in and the height is in. (Round to the nearest hundredth.) h Volume of a cylinder = r²h Lateral area of a cylinder = 2лrharrow_forwardFind the derivative of the following function. -8e5x y= 9x+2arrow_forwardExplain how to solve all solutions of y"(x)+ay'(x)+by(x)=0 when the Characteristic Equation λ2+aλ+b=0 of the second-order linear differential equation y"(x)+ay'(x)+by(x)=0 has no real roots. Please distinguish between the two methods of "using real numbers to solve the space base" and "using complex numbers to solve the space base" and explain the key points respectively.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL

Elementary Geometry For College Students, 7e
Geometry
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Cengage,

Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Double and Triple Integrals; Author: Professor Dave Explains;https://www.youtube.com/watch?v=UubU3U2C8WM;License: Standard YouTube License, CC-BY