Explanation Given: ∫ 0 8 ∫ 1 2 x d x d y x 2 + y Calculation: Step 1: ∫ 1 2 x d x x 2 + y Compute the indefinite integral ∫ x d x x 2 + y Apply u substitution: u = x 2 + y = ∫ d u 2 u Apply the power rule: = 1 2 . u − 1 2 + 1 − 1 2 + 1 = 1 2 . ( x 2 + y ) − 1 2 + 1 − 1 2 + 1 = x 2 + y + C Step 2: Compute the boundaries ∫ 1 2 x d x x 2 + y Formula used: ∫ a b f ( x ) d x = F ( b ) − F ( a ) = lim x → b − ( F ( x ) ) - lim x → a + ( F ( x ) ) lim x → 1 + ( x 2 + y ) = y + 1 lim x → 2 − ( x 2 + y ) = y + ...

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ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 16.1, Problem 34E

To determine

Evaluate the iterated integral $\int_{0}^{8} \int_{1}^{2} \frac{x d x d y}{\sqrt{x^{2} + y}}$

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Chapter 16.1, Problem 33E

Chapter 16.1, Problem 35E

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Chapter 16 Solutions

CALCULUS (CLOTH)

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