Explanation Formula used: If f is a polar rectangle R given by 0 ≤ a ≤ r ≤ b , α ≤ θ ≤ β where 0 ≤ β − α ≤ 2 π , then, ∬ R f ( x , y ) d A = ∫ α β ∫ a b f ( r cos θ , r sin θ ) r d r d θ … … ( 1 ) Calculation: Since the given region is the semi annulus, it is easier to use polar coordinates. From the figure given in the problem, it is observed that radius r ranges from 3 to 6 and θ varies from − π 2 to π 2

Bundle: Stewart, Essential Calculus: Early Transcendentals, 2nd (hardound) + WebAssign Printed Access Card for Stewart's Essential Calculus: Early ... Multi-Term + WebAssign - Start Smart Guide

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ISBN: 9781133425946

Author: James Stewart

Publisher: Cengage Learning

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Chapter 12.3, Problem 4E

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To write: An iterated integral by deciding whether to use polar coordinates or rectangular coordinates.

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Chapter 12.3, Problem 3E

Chapter 12.3, Problem 5E

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Chapter 12 Solutions

Bundle: Stewart, Essential Calculus: Early Transcendentals, 2nd (hardound) + WebAssign Printed Access Card for Stewart's Essential Calculus: Early ... Multi-Term + WebAssign - Start Smart Guide

Ch. 12.1 - (a) Estimate the volume of the solid that lies...Ch. 12.1 - If R = [0, 4] [1, 2], use a Riemann sum with m =...Ch. 12.1 - (a) Use a Riemann sum with m = n = 2 to estimate...Ch. 12.1 - (a) Estimate the volume of the solid that lies...Ch. 12.1 - A 20-ft-by-30-ft swimming pool is filled with...Ch. 12.1 - A contour map is shown for a function f on the...Ch. 12.1 - 79 Evaluate the double integral by first...Ch. 12.1 - 7-9 Evaluate the double integral by first...Ch. 12.1 - Evaluate the double integral by first identifying...Ch. 12.1 - The integral R9y2dA, where R = [0, 4] [0, 2],...

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An iterated integral by deciding whether to use polar coordinates or rectangular coordinates.

Solution Summary: The author explains how to write an iterated integral by deciding whether to use polar or rectangular coordinates.

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To write: An iterated integral by deciding whether to use polar coordinates or rectangular coordinates.

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Chapter 12 Solutions