Calculus With Applications, Books a la Carte Plus MyLab Math Package (11th Edition)
11th Edition
ISBN: 9780133886849
Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey
Publisher: PEARSON
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Chapter 8.4, Problem 2YT
To determine
To find: The value of the improper
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3. (i) Using the definition of the line integral of a vector field, calculate the
line integral
L³
F.dy
of the vector field F: R² → R² given by
F(x, y) = (y, x),
and where the curve & is the unit semi-circle centred at the origin, located in
the upper half-plane and oriented in the anticlockwise direction.
Hint. Represent the curve y as the join of two curves y = 71 + 1/2 (see Example 8.9
in the Notes).
[20 Marks]
(ii) Calculate the same integral using Green's Theorem.
[10 Marks]
1. Evaluate the integral
↓ f(x, y)dxdy,
of function f R² →R over the domain DC R2, where:
f(x, y) = 2x + y
and D is the is the triangle with vertices (0, -1), (1,0) and (0,2).
Hint. Represent D in the form D = {(x, y) = R² : x = (a, b), g(x) < y < h(x)} for
some a
2. (i) Describe with a sketch the trace of the following curve in R²
(t) = (t² sin(t), t2 cos(t)),
(€ -2,2]).
[15 Marks]
(ii) Find the length of this curve.
[25 Marks]
Chapter 8 Solutions
Calculus With Applications, Books a la Carte Plus MyLab Math Package (11th Edition)
Ch. 8.1 - YOUR TURN 1 Find
Ch. 8.1 - YOUR TURN 2 Find
Ch. 8.1 - YOUR TURN 3
Find
Ch. 8.1 - YOUR TURN 4 Find
.
Ch. 8.1 - YOUR TURN 5
Find
Ch. 8.1 - Prob. 1WECh. 8.1 - Find the following.
W2.
Ch. 8.1 - Find the following.
W3.
Ch. 8.1 - Find the following.
W4.
Ch. 8.1 - Use integration by parts to find the integrals in...
Ch. 8.1 - Prob. 6WECh. 8.1 - Use integration by parts to find the integrals in...Ch. 8.1 - Use integration by parts to find the integrals in...Ch. 8.1 - Use integration by parts to find the integrals in...Ch. 8.1 - Use integration by parts to find the integrals in...Ch. 8.1 - Use integration by parts to find the integrals in...Ch. 8.1 - Use integration by parts to find the integrals in...Ch. 8.1 - Use integration by parts to find the integrals in...Ch. 8.1 - Use integration by parts to find the integrals in...Ch. 8.1 - Use integration by parts to find the integrals in...Ch. 8.1 - Use integration by parts to find the integrals in...Ch. 8.1 - Use integration by parts to find the integrals in...Ch. 8.1 - Prob. 12ECh. 8.1 - Exercises 13–22 are mixed—some require integration...Ch. 8.1 - Exercises 13–22 are mixed—some require integration...Ch. 8.1 - Exercises 13–22 are mixed—some require integration...Ch. 8.1 - Exercises 13–22 are mixed—some require integration...Ch. 8.1 - Exercises 13–22 are mixed—some require integration...Ch. 8.1 - Exercises 13–22 are mixed—some require integration...Ch. 8.1 - Exercises 13–22 are mixed—some require integration...Ch. 8.1 - Prob. 20ECh. 8.1 - Exercises 13–22 are mixed—some require integration...Ch. 8.1 - Prob. 22ECh. 8.1 - Prob. 23ECh. 8.1 - Prob. 24ECh. 8.1 - Prob. 25ECh. 8.1 - Prob. 26ECh. 8.1 - Prob. 27ECh. 8.1 - Prob. 28ECh. 8.1 - Prob. 29ECh. 8.1 - Prob. 30ECh. 8.1 - 31. Suppose that u and v are differentiable...Ch. 8.1 - 32. Suppose that u and v are differentiable...Ch. 8.1 - Prob. 33ECh. 8.1 - Prob. 34ECh. 8.1 - 35. Use integration by parts to derive the...Ch. 8.1 - 36. Use integration by parts to derive the...Ch. 8.1 - Prob. 37ECh. 8.1 - 38. Using integration by parts,
Subtracting from...Ch. 8.1 - 39. Rate of Change of Revenue The rate of change...Ch. 8.1 - 40. Reaction to a Drug The rate of reaction to a...Ch. 8.1 - 41. Growth of a Population The rate of growth of a...Ch. 8.1 - 42. APPLY IT Rate of Growth The area covered by a...Ch. 8.1 - 43. Thermic Effect of Food As we saw in an earlier...Ch. 8.1 - 44. Rumen Fermentation The rumen is the first...Ch. 8.2 - YOUR TURN 1 Find the volume of the solid of...Ch. 8.2 - Prob. 2YTCh. 8.2 - Prob. 1WECh. 8.2 - Prob. 2WECh. 8.2 - Find the following.
W3.
Ch. 8.2 - Prob. 4WECh. 8.2 - Find the following.
W5. (Sec. 15.4)
Ch. 8.2 - Prob. 6WECh. 8.2 - Prob. 1ECh. 8.2 - Prob. 2ECh. 8.2 - Find the volume of the solid of revolution formed...Ch. 8.2 - Find the volume of the solid of revolution formed...Ch. 8.2 - Find the volume of the solid of revolution formed...Ch. 8.2 - Find the volume of the solid of revolution formed...Ch. 8.2 - Find the volume of the solid of revolution formed...Ch. 8.2 - Find the volume of the solid of revolution formed...Ch. 8.2 - Find the volume of the solid of revolution formed...Ch. 8.2 - Find the volume of the solid of revolution formed...Ch. 8.2 - Find the volume of the solid of revolution formed...Ch. 8.2 - Find the volume of the solid of revolution formed...Ch. 8.2 - Find the volume of the solid of revolution formed...Ch. 8.2 - Find the volume of the solid of revolution formed...Ch. 8.2 - Find the volume of the solid of revolution formed...Ch. 8.2 - Find the volume of the solid of revolution formed...Ch. 8.2 - Find the volume of the solid of revolution formed...Ch. 8.2 - Prob. 18ECh. 8.2 - Prob. 19ECh. 8.2 - Prob. 20ECh. 8.2 - The function defined by has as its graph a...Ch. 8.2 - Prob. 22ECh. 8.2 - Prob. 23ECh. 8.2 - Prob. 24ECh. 8.2 - Find the average value of each function on the...Ch. 8.2 - Find the average value of each function on the...Ch. 8.2 - Find the average value of each function on the...Ch. 8.2 - Find the average value of each function on the...Ch. 8.2 - Find the average value of each function on the...Ch. 8.2 - Find the average value of each function on the...Ch. 8.2 - Find the average value of each function on the...Ch. 8.2 - Prob. 32ECh. 8.2 - Prob. 33ECh. 8.2 - 34. Average Price David Lopez plots the price per...Ch. 8.2 - 35. Average Price A stock analyst plots the price...Ch. 8.2 - Prob. 36ECh. 8.2 - 37. Average Inventory The DeMarco Pasta Company...Ch. 8.2 - 38. Public Debt In Example 5 of Section 10.3. the...Ch. 8.2 - Prob. 39ECh. 8.2 - 40. Blood Flow The figure shows the blood flow in...Ch. 8.2 - 41. Drug Reaction The intensity of the reaction to...Ch. 8.2 - Prob. 42ECh. 8.2 - 43. Production Rate Suppose the number of items a...Ch. 8.2 - 44. Typing Speed The function describes a...Ch. 8.2 - Prob. 45ECh. 8.3 - YOUR TURN 1 Find the total income over the first 2...Ch. 8.3 - YOUR TURN 2
Find the present value of an income...Ch. 8.3 - Prob. 3YTCh. 8.3 - Prob. 4YTCh. 8.3 - Prob. 1WECh. 8.3 - Prob. 2WECh. 8.3 - Prob. 3WECh. 8.3 - Prob. 4WECh. 8.3 - Prob. 1ECh. 8.3 - Each of the functions in Exercises 1–14 represents...Ch. 8.3 - Each of the functions in Exercises 1–14 represents...Ch. 8.3 - Each of the functions in Exercises 1–14 represents...Ch. 8.3 - Each of the functions in Exercises 1–14 represents...Ch. 8.3 - Each of the functions in Exercises 1–14 represents...Ch. 8.3 - Prob. 7ECh. 8.3 - Prob. 8ECh. 8.3 - Prob. 9ECh. 8.3 - Each of the functions in Exercises 1–14 represents...Ch. 8.3 - Prob. 11ECh. 8.3 - Each of the functions in Exercises 1–14 represents...Ch. 8.3 - Each of the functions in Exercises 1–14 represents...Ch. 8.3 - Each of the functions in Exercises 1–14 represents...Ch. 8.3 - 15. Accumulated Amount of Money Flow An investment...Ch. 8.3 - 16. Present Value A real estate investment is...Ch. 8.3 - 17. Money Flow The rate of a continuous (low of...Ch. 8.3 - 18. Money Flow The rate of a continuous money flow...Ch. 8.3 - 19. Present Value A money market fund has a...Ch. 8.3 - 20. Accumulated Amount of Money Flow Find the...Ch. 8.4 - YOUR TURN 1
Find each integral.
(a)
(b)
Ch. 8.4 - Prob. 2YTCh. 8.4 - Prob. 1WECh. 8.4 - Prob. 2WECh. 8.4 - Prob. 3WECh. 8.4 - Prob. 4WECh. 8.4 - Prob. 1ECh. 8.4 - Prob. 2ECh. 8.4 - Determine whether each improper integral converges...Ch. 8.4 - Determine whether each improper integral converges...Ch. 8.4 - Determine whether each improper integral converges...Ch. 8.4 - Prob. 6ECh. 8.4 - Determine whether each improper integral converges...Ch. 8.4 - Prob. 8ECh. 8.4 - Determine whether each improper integral converges...Ch. 8.4 - Prob. 10ECh. 8.4 - Determine whether each improper integral converges...Ch. 8.4 - Prob. 12ECh. 8.4 - Determine whether each improper integral converges...Ch. 8.4 - Prob. 14ECh. 8.4 - Determine whether each improper integral converges...Ch. 8.4 - Determine whether each improper integral converges...Ch. 8.4 - Determine whether each improper integral converges...Ch. 8.4 - Prob. 18ECh. 8.4 - Determine whether each improper integral converges...Ch. 8.4 - Prob. 20ECh. 8.4 - Determine whether each improper integral converges...Ch. 8.4 - Prob. 22ECh. 8.4 - Determine whether each improper integral converges...Ch. 8.4 - Prob. 24ECh. 8.4 - Determine whether each improper integral converges...Ch. 8.4 - Determine whether each improper integral converges...Ch. 8.4 - Prob. 27ECh. 8.4 - Prob. 28ECh. 8.4 - Prob. 29ECh. 8.4 - Prob. 30ECh. 8.4 - Prob. 31ECh. 8.4 - Prob. 32ECh. 8.4 - Prob. 33ECh. 8.4 - Prob. 34ECh. 8.4 - 35. Find .
Ch. 8.4 - Prob. 36ECh. 8.4 - Prob. 37ECh. 8.4 - Prob. 38ECh. 8.4 - Prob. 39ECh. 8.4 - Prob. 40ECh. 8.4 - Prob. 41ECh. 8.4 - Capital Value Find the capital values of the...Ch. 8.4 - Prob. 43ECh. 8.4 - Prob. 44ECh. 8.4 - 45. Capital Value An investment produces a...Ch. 8.4 - 46. Capital Value Suppose income from an...Ch. 8.4 - Prob. 47ECh. 8.4 - Prob. 48ECh. 8.4 - 49. Drug Reaction The rate of reaction to a drug...Ch. 8.4 - Prob. 50ECh. 8.4 - Prob. 51ECh. 8.4 - Radioactive Waste The rate at which radioactive...Ch. 8.4 - Prob. 53ECh. 8.4 - 54. Gamma Function An important function in many...Ch. 8 - Prob. 1RECh. 8 - Prob. 2RECh. 8 - Prob. 3RECh. 8 - Prob. 4RECh. 8 - Prob. 5RECh. 8 - Prob. 6RECh. 8 - Prob. 7RECh. 8 - Prob. 8RECh. 8 - Prob. 9RECh. 8 - Prob. 10RECh. 8 - Prob. 11RECh. 8 - Prob. 12RECh. 8 - Prob. 13RECh. 8 - Prob. 14RECh. 8 - Prob. 15RECh. 8 - Prob. 16RECh. 8 - Prob. 17RECh. 8 - Prob. 18RECh. 8 - Prob. 19RECh. 8 - Prob. 20RECh. 8 - Prob. 21RECh. 8 - Prob. 22RECh. 8 - Prob. 23RECh. 8 - Prob. 24RECh. 8 - Prob. 25RECh. 8 - Prob. 26RECh. 8 - Prob. 27RECh. 8 - Prob. 28RECh. 8 - Prob. 29RECh. 8 - Prob. 30RECh. 8 - Prob. 31RECh. 8 - Prob. 32RECh. 8 - Prob. 33RECh. 8 - Prob. 34RECh. 8 - Prob. 35RECh. 8 - Prob. 36RECh. 8 - Prob. 37RECh. 8 - Prob. 38RECh. 8 - Prob. 39RECh. 8 - Prob. 40RECh. 8 - Prob. 41RECh. 8 - Prob. 42RECh. 8 - Prob. 43RECh. 8 - Prob. 44RECh. 8 - Prob. 45RECh. 8 - Prob. 46RECh. 8 - Prob. 47RECh. 8 - Prob. 48RECh. 8 - Prob. 49RECh. 8 - Prob. 50RECh. 8 - Prob. 51RECh. 8 - Prob. 52RECh. 8 - Prob. 53RECh. 8 - Prob. 54RECh. 8 - Prob. 55RECh. 8 - Prob. 56RECh. 8 - Prob. 57RECh. 8 - Prob. 58RECh. 8 - Prob. 59RECh. 8 - Prob. 60RECh. 8 - Prob. 61RE
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