Explanation Given: ∫ 0 1 ∫ 0 2 ( x + 4 y 3 ) d x d y Calculation: Step 1: ∫ 0 2 x + 4 y 3 d x = 8 y 3 + 2 ∫ 0 2 x + 4 y 3 d x Compute the indefinite integral ∫ x + 4 y 3 d x = x 2 2 + 4 y 3 x + C ∫ x + 4 y 3 d x (Adding a constant to a solution) Step 2: Apply the sum rule ∫ x d x + ∫ 4 y 3 d x ∫ x d x = x 2 2 ∫ x d x Step3: Apply the power rule: ∫ x a d x = x a + 1 a + 1 , a ≠ − 1 x 1 + 1 1 + 1 Simplify: x 2 2 Step 2: ∫ 4 y 3 d x Integral of a constant: ∫ a d x = a x 4

4th Edition

ISBN: 9781319055844

Author: FRANZOSA

Publisher: VST

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Chapter 16.1, Problem 27E

To determine

The value of the iterated integral $\int_{0}^{1} \int_{0}^{2} (x + 4 y^{3}) d x d y$

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Chapter 16.1, Problem 26E

Chapter 16.1, Problem 28E

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Chapter 16 Solutions

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