Multivariable Calculus
8th Edition
ISBN: 9781305266643
Author: James Stewart
Publisher: Cengage Learning
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Chapter 17.2, Problem 4E
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To solve: The
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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.
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.
Chapter 17 Solutions
Multivariable Calculus
Ch. 17.1 - Solve the differential equation. 1. y" y' 6y = 0Ch. 17.1 - Prob. 2ECh. 17.1 - Prob. 3ECh. 17.1 - Solve the differential equation. 4. y" + y' 12y =...Ch. 17.1 - Prob. 5ECh. 17.1 - Prob. 6ECh. 17.1 - Prob. 7ECh. 17.1 - Prob. 8ECh. 17.1 - Solve the differential equation. 9. y" 4y' + 13y...Ch. 17.1 - Prob. 10E
Ch. 17.1 - Prob. 11ECh. 17.1 - Prob. 12ECh. 17.1 - Prob. 13ECh. 17.1 - Prob. 14ECh. 17.1 - Prob. 15ECh. 17.1 - Prob. 16ECh. 17.1 - Prob. 17ECh. 17.1 - Prob. 18ECh. 17.1 - Solve the initial-value problem. 19. 9y" + 12y' +...Ch. 17.1 - Prob. 20ECh. 17.1 - Prob. 21ECh. 17.1 - Prob. 22ECh. 17.1 - Solve the initial-value problem. 23. y" y' 12y =...Ch. 17.1 - Solve the initial-value problem. 24. 4y" + 4y' +...Ch. 17.1 - Prob. 25ECh. 17.1 - Prob. 26ECh. 17.1 - Prob. 27ECh. 17.1 - Prob. 28ECh. 17.1 - Prob. 29ECh. 17.1 - Prob. 30ECh. 17.1 - Prob. 31ECh. 17.1 - Solve the boundary-value problem, if possible. 32....Ch. 17.1 - Prob. 33ECh. 17.1 - If a, b, and c are all positive constants and y(x)...Ch. 17.2 - Prob. 1ECh. 17.2 - Prob. 2ECh. 17.2 - Prob. 3ECh. 17.2 - Prob. 4ECh. 17.2 - Prob. 5ECh. 17.2 - Prob. 6ECh. 17.2 - Prob. 7ECh. 17.2 - Prob. 8ECh. 17.2 - Prob. 9ECh. 17.2 - Prob. 10ECh. 17.2 - Prob. 11ECh. 17.2 - Prob. 12ECh. 17.2 - Prob. 13ECh. 17.2 - Prob. 14ECh. 17.2 - Prob. 15ECh. 17.2 - Prob. 16ECh. 17.2 - Prob. 17ECh. 17.2 - Prob. 18ECh. 17.2 - Prob. 19ECh. 17.2 - Prob. 20ECh. 17.2 - Solve the differential equation using (a)...Ch. 17.2 - Prob. 22ECh. 17.2 - Prob. 23ECh. 17.2 - Solve the differential equation using the method...Ch. 17.2 - Solve the differential equation using the method...Ch. 17.2 - Solve the differential equation using the method...Ch. 17.2 - Prob. 27ECh. 17.2 - Prob. 28ECh. 17.3 - A spring has natural length 0.75 m and a 5-kg...Ch. 17.3 - Prob. 2ECh. 17.3 - A spring with a mass of 2 kg has damping constant...Ch. 17.3 - Prob. 4ECh. 17.3 - Prob. 5ECh. 17.3 - Prob. 6ECh. 17.3 - Prob. 7ECh. 17.3 - Prob. 8ECh. 17.3 - Suppose a spring has mass m and spring constant k...Ch. 17.3 - Prob. 10ECh. 17.3 - Prob. 11ECh. 17.3 - Prob. 12ECh. 17.3 - Prob. 13ECh. 17.3 - Prob. 14ECh. 17.3 - Prob. 15ECh. 17.3 - The battery in Exercise 14 is replaced by a...Ch. 17.3 - Prob. 17ECh. 17.3 - Prob. 18ECh. 17.4 - Prob. 1ECh. 17.4 - Prob. 2ECh. 17.4 - Prob. 3ECh. 17.4 - Prob. 4ECh. 17.4 - Prob. 5ECh. 17.4 - Prob. 6ECh. 17.4 - Prob. 7ECh. 17.4 - Prob. 8ECh. 17.4 - Prob. 9ECh. 17.4 - Prob. 10ECh. 17.4 - Prob. 11ECh. 17.4 - Prob. 12ECh. 17 - (a) Write the general form of a second-order...Ch. 17 - Prob. 2RCCCh. 17 - (a) Write the general form of a second-order...Ch. 17 - Prob. 4RCCCh. 17 - Prob. 5RCCCh. 17 - Prob. 1RQCh. 17 - Prob. 2RQCh. 17 - Prob. 3RQCh. 17 - Prob. 4RQCh. 17 - Solve the differential equation. 1. 4y" y =0Ch. 17 - Prob. 2RECh. 17 - Prob. 3RECh. 17 - Solve the differential equation. 4. y" + 8y' + 16y...Ch. 17 - Prob. 5RECh. 17 - Prob. 6RECh. 17 - Prob. 7RECh. 17 - Prob. 8RECh. 17 - Prob. 9RECh. 17 - Solve the differential equation. 10....Ch. 17 - Prob. 11RECh. 17 - Solve the initial-value problem. 12. y" 6y' + 25y...Ch. 17 - Solve the initial-value problem. 13. y" 5y' + 4y...Ch. 17 - Prob. 14RECh. 17 - Solve the boundary-value problem, if possible. 15....Ch. 17 - Prob. 16RECh. 17 - Prob. 17RECh. 17 - Prob. 18RECh. 17 - A series circuit contains a resistor with R = 40 ,...Ch. 17 - Prob. 20RECh. 17 - Assume that the earth is a solid sphere of uniform...
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- Evaluate 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_forwardLet 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_forward
- Let 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_forwardplease show all the workarrow_forward
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