Explanation Given : f ( x , y ) = cos ( 2 x + y ) , Domain D as region over 1 2 ≤ x ≤ π 2 , 1 ≤ y ≤ 2 x Calculation : Step 1: The given inequalities describe D as a vertically simple region Step 2: Computing the double integral of f ( x , y ) = cos ( 2 x + y ) on D by the following iterated integral as stated in Theorem 2, we get ∫ ∫ D cos ( 2 x + y ) d A = ∫ 1 / 2 π / 2 ∫ 1 2 x cos ( 2 x + y ) d y d x = ∫ 1 / 2 π / 2 s i n ( 2 x + y ) | y = 1 2 x

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 16.2, Problem 20E

To determine

The value of the double integral of $f (x, y) = \cos (2 x + y)$ over the domain D indicated as $\frac{1}{2} \leq x \leq \frac{π}{2}, 1 \leq y \leq 2 x$

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Chapter 16.2, Problem 19E

Chapter 16.2, Problem 21E

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Chapter 16 Solutions

CALCULUS (CLOTH)

Ch. 16.1 - Prob. 1PQ Ch. 16.1 - Prob. 2PQ Ch. 16.1 - Prob. 3PQ Ch. 16.1 - Prob. 4PQ Ch. 16.1 - Prob. 5PQ Ch. 16.1 - Prob. 6PQ Ch. 16.1 - Prob. 1E Ch. 16.1 - Prob. 2E Ch. 16.1 - Prob. 3E Ch. 16.1 - Prob. 4E

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The value of the double integral of f ( x , y ) = cos ( 2 x + y ) over the domain D indicated as 1 2 ≤ x ≤ π 2 , 1 ≤ y ≤ 2 x

Solution Summary: The author calculates the value of the double integral of f ( x, y ) = cos over the domain D by the following iterated integral as stated in Theorem 2.

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The value of the double integral of $f (x, y) = \cos (2 x + y)$ over the domain D indicated as $\frac{1}{2} \leq x \leq \frac{π}{2}, 1 \leq y \leq 2 x$

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Chapter 16 Solutions

The value of the double integral of f ( x , y ) = cos ( 2 x + y ) over the domain D indicated as 1 2 ≤ x ≤ π 2 , 1 ≤ y ≤ 2 x

Solution Summary: The author calculates the value of the double integral of f ( x, y ) = cos over the domain D by the following iterated integral as stated in Theorem 2.

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The value of the double integral of f(x,y)=cos(2x+y) over the domain D indicated as 12≤x≤π2,1≤y≤2x

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Chapter 16 Solutions

The value of the double integral of $f (x, y) = \cos (2 x + y)$ over the domain D indicated as $\frac{1}{2} \leq x \leq \frac{π}{2}, 1 \leq y \leq 2 x$