Explanation Given: ∫ 0 4 ∫ 0 5 d y d x x + y Calculation: Step 1: ∫ 0 5 d y x + y Compute the indefinite integral ∫ d y x + y ∫ d y x + y Apply u substitution: u = x + y = ∫ d u u = ∫ u − 1 2 d u Apply the power rule: = u − 1 2 + 1 − 1 2 + 1 = ( x + y ) − 1 2 + 1 − 1 2 + 1 = 2 x + y + C Step 2: Compute the boundaries ∫ 0 5 d y x + y Formula used: ∫ a b f ( x ) d x = F ( b ) − F ( a ) = lim x → b − ( F ( x ) ) - lim x → a + ( F ( x ) ) lim y → 0 + ( 2 x + y ) = 2 x lim y → 5 − ( 2 x + y ) = 2 x + 5 ∫ 0 5 d y x + y = 2 x + 5 - 2 x = 2 ( x + 5 − x )

4th Edition

ISBN: 9781319323394

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 16.1, Problem 33E

To determine

Evaluate the iterated integral $\int_{0}^{4} \int_{0}^{5} \frac{d y d x}{\sqrt{x + y}}$

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Chapter 16.1, Problem 32E

Chapter 16.1, Problem 34E

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Chapter 16 Solutions

CALCULUS W/SAPLING ACCESS >IC<

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Evaluate the iterated integral ∫ 0 4 ∫ 0 5 d y d x x + y

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