Explanation Given: ∫ 0 4 ∫ 0 9 x + 4 y d x d y Calculation: Step 1: ∫ 0 9 x + 4 y d x Compute the indefinite integral = ∫ x + 4 y d x = 2 3 ( x + 4 y ) 3 2 + C = ∫ x + 4 y d x Step 2: Apply u-substitution: u = x + 4 y = ∫ u d u Step 3 : Apply the power rule: ∫ x a d x = x a + 1 a + 1 , a ≠ − 1 = u 1 2 + 1 1 2 + 1 Substitute back u = x + 4 y = ( x + 4 y ) 1 2 + 1 1 2 + 1 Simplify: Join 1 2 + 1 : 3 2 ( x + 4 y ) 1 2 + 1 3 2 ( x + 4 y ) 3 2 3 2 Step 4: Apply the fraction rule: a b c = a . c b 2 ( 4 y + x ) 3 2 3 2 3 ( x + 4 y ) 3 2 Step 5: Add a constant to the solution: 2 3 ( x + 4 y ) 3 2 + C Compute the boundaries: lim x → 0 + ( 2 3 ( x + 4 y ) 3 2 ) = 16 3 y 3 2 lim x → 9 − ( 2 3 ( x + 4 y ) 3 2 ) = 2 3 ( 9 + 4 y ) 3 2 2 3 ( 9 + 4 y ) 3 2 - 16 3 y 3 2 Step 6 : Simplify 2 3 ( 9 + 4 y ) 3 2 - 16 3 y 3 2 ∫ 0 4 2 3 ( ( 4 y + 9 ) 3 2 − 8 y 3 2 ) d y Step 7 : Compute the indefinite integral: ∫ 2 3 ( ( 4 y + 9 ) 3 2 − 8 y 3 2 ) d y Take the constant out: 2 3 ...

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 16.1, Problem 29E

To determine

The value of the iterated integral $\int_{0}^{4} \int_{0}^{9} \sqrt{x + 4 y} d x d y$

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Chapter 16.1, Problem 28E

Chapter 16.1, Problem 30E

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Chapter 16 Solutions

CALCULUS (CLOTH)

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The value of the iterated integral ∫ 0 4 ∫ 0 9 x + 4 y d x d y

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The value of the iterated integral $\int_{0}^{4} \int_{0}^{9} \sqrt{x + 4 y} d x d y$

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Chapter 16 Solutions

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