Precalculus: A Unit Circle Approach
2nd Edition
ISBN: 9780321825391
Author: Ratti
Publisher: PEARSON
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Chapter A.2, Problem 18E
To determine
To perform the indicated operations.
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Evaluate the following integral over the Region R.
(Answer accurate to 2 decimal places).
√ √(x + y) A
R
R = {(x, y) | 25 < x² + y² ≤ 36, x < 0}
Hint: The integral and Region is defined in rectangular coordinates.
Find the volume of the solid that lies under the paraboloid z = 81 - x² - y² and within the cylinder
(x − 1)² + y² = 1. A plot of an example of a similar solid is shown below. (Answer accurate to 2
decimal places).
Volume using Double Integral
Paraboloid & Cylinder
-3
Hint: The integral and region is defined in polar coordinates.
Evaluate the following integral over the Region R.
(Answer accurate to 2 decimal places).
√4(1–2²
4(1 - x² - y²) dA
R
3
R = {(r,0) | 0 ≤ r≤ 2,0π ≤0≤¼˜}.
Hint: The integral is defined in rectangular coordinates. The Region is defined in polar coordinates.
Chapter A.2 Solutions
Precalculus: A Unit Circle Approach
Ch. A.2 - In Exercises 1-4, determine whether the given...Ch. A.2 - In Exercises 1-4, determine whether the given...Ch. A.2 - In Exercises 1-4, determine whether the given...Ch. A.2 - Prob. 4ECh. A.2 - In Exercises 5-8, find the degree and list the...Ch. A.2 - Prob. 6ECh. A.2 - Prob. 7ECh. A.2 - Prob. 8ECh. A.2 - In Exercises 9-16, perform the indicated...Ch. A.2 - In Exercises 9-16, perform the indicated...
Ch. A.2 - In Exercises 9-16, perform the indicated...Ch. A.2 - Prob. 12ECh. A.2 - Prob. 13ECh. A.2 - Prob. 14ECh. A.2 - Prob. 15ECh. A.2 - Prob. 16ECh. A.2 - Prob. 17ECh. A.2 - Prob. 18ECh. A.2 - Prob. 19ECh. A.2 - Prob. 20ECh. A.2 - Prob. 21ECh. A.2 - In Exercises 17-50, perform the indicated...Ch. A.2 - Prob. 23ECh. A.2 - Prob. 24ECh. A.2 - In Exercises 17-50, perform the indicated...Ch. A.2 - Prob. 26ECh. A.2 - Prob. 27ECh. A.2 - Prob. 28ECh. A.2 - Prob. 29ECh. A.2 - Prob. 30ECh. A.2 - Prob. 31ECh. A.2 - Prob. 32ECh. A.2 - Prob. 33ECh. A.2 - Prob. 34ECh. A.2 - Prob. 35ECh. A.2 - In Exercises 17-50, perform the indicated...Ch. A.2 - Prob. 37ECh. A.2 - Prob. 38ECh. A.2 - Prob. 39ECh. A.2 - In Exercises 17-50, perform the indicated...Ch. A.2 - Prob. 41ECh. A.2 - Prob. 42ECh. A.2 - In Exercises 17-50, perform the indicated...Ch. A.2 - In Exercises 17-50, perform the indicated...Ch. A.2 - In Exercises 17-50, perform the indicated...Ch. A.2 - Prob. 46ECh. A.2 - Prob. 47ECh. A.2 - Prob. 48ECh. A.2 - Prob. 49ECh. A.2 - Prob. 50ECh. A.2 - Prob. 51ECh. A.2 - Prob. 52ECh. A.2 - Prob. 53ECh. A.2 - Prob. 54ECh. A.2 - Prob. 55ECh. A.2 - Prob. 56ECh. A.2 - Prob. 57ECh. A.2 - Prob. 58ECh. A.2 - Prob. 59ECh. A.2 - Prob. 60ECh. A.2 - In Exercises 61-108, factor each polynomial...Ch. A.2 - In Exercises 61-108, factor each polynomial...Ch. A.2 - In Exercises 61-108, factor each polynomial...Ch. A.2 - In Exercises 61-108, factor each polynomial...Ch. A.2 - In Exercises 61-108, factor each polynomial...Ch. A.2 - Prob. 66ECh. A.2 - In Exercises 61-108, factor each polynomial...Ch. A.2 - Prob. 68ECh. A.2 - Prob. 69ECh. A.2 - Prob. 70ECh. A.2 - In Exercises 61-108, factor each polynomial...Ch. A.2 - In Exercises 61-108, factor each polynomial...Ch. A.2 - In Exercises 61-108, factor each polynomial...Ch. A.2 - In Exercises 61-108, factor each polynomial...Ch. A.2 - Prob. 75ECh. A.2 - In Exercises 61-108, factor each polynomial...Ch. A.2 - In Exercises 61-108, factor each polynomial...Ch. A.2 - In Exercises 61-108, factor each polynomial...Ch. A.2 - In Exercises 61-108, factor each polynomial...Ch. A.2 - In Exercises 61-108, factor each polynomial...Ch. A.2 - Prob. 81ECh. A.2 - Prob. 82ECh. A.2 - Prob. 83ECh. A.2 - Prob. 84ECh. A.2 - In Exercises 61-108, factor each polynomial...Ch. A.2 - Prob. 86ECh. A.2 - Prob. 87ECh. A.2 - In Exercises 61-108, factor each polynomial...Ch. A.2 - In Exercises 61-108, factor each polynomial...Ch. A.2 - In Exercises 61-108, factor each polynomial...Ch. A.2 - In Exercises 61-108, factor each polynomial...Ch. A.2 - In Exercises 61-108, factor each polynomial...Ch. A.2 - In Exercises 61-108, factor each polynomial...Ch. A.2 - Prob. 94ECh. A.2 - Prob. 95ECh. A.2 - Prob. 96ECh. A.2 - Prob. 97ECh. A.2 - Prob. 98ECh. A.2 - Prob. 99ECh. A.2 - Prob. 100ECh. A.2 - Prob. 101ECh. A.2 - Prob. 102ECh. A.2 - Prob. 103ECh. A.2 - Prob. 104ECh. A.2 - Prob. 105ECh. A.2 - Prob. 106ECh. A.2 - Prob. 107ECh. A.2 - Prob. 108ECh. A.2 - Prob. 109ECh. A.2 - Prob. 110ECh. A.2 - Prob. 111ECh. A.2 - Prob. 112ECh. A.2 - Prob. 113ECh. A.2 - In Exercises 61-108, factor each polynomial...Ch. A.2 - In Exercises 61-108, factor each polynomial...Ch. A.2 - Prob. 116ECh. A.2 - Prob. 117ECh. A.2 - Prob. 118ECh. A.2 - Prob. 119ECh. A.2 - Prob. 120ECh. A.2 - Prob. 121ECh. A.2 - In Exercises 61-108, factor each polynomial...Ch. A.2 - Prob. 123ECh. A.2 - Prob. 124ECh. A.2 - In Exercises 61-108, factor each polynomial...Ch. A.2 - Prob. 126ECh. A.2 - Prob. 127ECh. A.2 - Prob. 128ECh. A.2 - Prob. 129ECh. A.2 - Prob. 130ECh. A.2 - Prob. 131ECh. A.2 - Prob. 132ECh. A.2 - Prob. 133ECh. A.2 - Prob. 134ECh. A.2 - Prob. 135ECh. A.2 - Prob. 136ECh. A.2 - Prob. 137ECh. A.2 - Prob. 138ECh. A.2 - Prob. 139ECh. A.2 - Prob. 140ECh. A.2 - Prob. 141ECh. A.2 - Prob. 142ECh. A.2 - Prob. 143ECh. A.2 - Prob. 144E
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- Evaluate the following integral over the Region R. (Answer accurate to 2 decimal places). R - 1 · {(r,0) | 1 ≤ r≤ 5,½π≤ 0<1π}. Hint: Be sure to convert to Polar coordinates. Use the correct differential for Polar Coordinates.arrow_forwardEvaluate the following integral over the Region R. (Answer accurate to 2 decimal places). √ √2(x+y) dA R R = {(x, y) | 4 < x² + y² < 25,0 < x} Hint: The integral and Region is defined in rectangular coordinates.arrow_forwardHW: The frame shown in the figure is pinned at A and C. Use moment distribution method, with and without modifications, to draw NFD, SFD, and BMD. B I I 40 kN/m A 3 m 4 marrow_forward
- Let the region R be the area enclosed by the function f(x)= = 3x² and g(x) = 4x. If the region R is the base of a solid such that each cross section perpendicular to the x-axis is an isosceles right triangle with a leg in the region R, find the volume of the solid. You may use a calculator and round to the nearest thousandth. y 11 10 9 00 8 7 9 5 4 3 2 1 -1 -1 x 1 2arrow_forwardLet the region R be the area enclosed by the function f(x) = ex — 1, the horizontal line y = -4 and the vertical lines x = 0 and x = 3. Find the volume of the solid generated when the region R is revolved about the line y = -4. You may use a calculator and round to the nearest thousandth. 20 15 10 5 y I I I | I + -1.5 -1 -0.5 0.5 1 1.5 2 2.5 3 -5 I -10 -15 I + I I T I I + -20 I + -25 I I I -30 I 3.5 4 xarrow_forwardplease show all the workarrow_forward
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