Explanation Given : ∫ 0 4 ∫ y 2 4 x 2 + 5 y d x d y Calculation : Step 1: The limits of integration correspond to the inequalities describing the following shaded horizontally simple region: 0 ≤ y ≤ 4 , y ≤ x ≤ 2 Step 2: The region can also be expressed as a vertically simple region. Rewriting the equation x = y in the form y = x 2 , we define D by the following inequalities: 0 ≤ x ≤ 2 , 0 ≤ y ≤ x 2 Step 3: The corresponding iterated integral is ∫ 0 2 ∫ 0 x 2 4 x 2 + 5 y d y d x When we evaluate this integral ∫ 0 2 ∫ 0 x 2 4 x 2 + 5 y d y d x = ∫ 0 2 ( ∫ 0 x 2 ( 4 x 2 + 5 y ) 1 / 2 d y ) d x

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ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 16.2, Problem 29E

To determine

The sketch of the domain of integration of $\int_{0}^{4} \int_{\sqrt{y}}^{2} \sqrt{4 x^{2} + 5 y} d x d y$ and to evaluate the integration which is changed as an iterated integral in the opposite order.

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Chapter 16.2, Problem 28E

Chapter 16.2, Problem 30E

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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Prob. 2E Ch. 16.5 - Prob. 3E Ch. 16.5 - Prob. 4E Ch. 16.5 - Prob. 5E Ch. 16.5 - Prob. 6E Ch. 16.5 - Prob. 7E Ch. 16.5 - Prob. 8E Ch. 16.5 - Prob. 9E Ch. 16.5 - Prob. 10E Ch. 16.5 - Prob. 11E Ch. 16.5 - Prob. 12E Ch. 16.5 - Prob. 13E Ch. 16.5 - Prob. 14E Ch. 16.5 - Prob. 15E Ch. 16.5 - Prob. 16E Ch. 16.5 - Prob. 17E Ch. 16.5 - Prob. 18E Ch. 16.5 - Prob. 19E Ch. 16.5 - Prob. 20E Ch. 16.5 - Prob. 21E Ch. 16.5 - Prob. 22E Ch. 16.5 - Prob. 23E Ch. 16.5 - Prob. 24E Ch. 16.5 - Prob. 25E Ch. 16.5 - Prob. 26E Ch. 16.5 - Prob. 27E Ch. 16.5 - Prob. 28E Ch. 16.5 - Prob. 29E Ch. 16.5 - Prob. 30E Ch. 16.5 - Prob. 31E Ch. 16.5 - Prob. 32E Ch. 16.5 - Prob. 33E Ch. 16.5 - Prob. 34E Ch. 16.5 - Prob. 35E Ch. 16.5 - Prob. 36E Ch. 16.5 - Prob. 37E Ch. 16.5 - Prob. 38E Ch. 16.5 - Prob. 39E Ch. 16.5 - Prob. 40E Ch. 16.5 - Prob. 41E Ch. 16.5 - Prob. 42E Ch. 16.5 - Prob. 43E Ch. 16.5 - Prob. 44E Ch. 16.5 - Prob. 45E Ch. 16.5 - Prob. 46E Ch. 16.5 - Prob. 47E Ch. 16.5 - Prob. 48E Ch. 16.5 - Prob. 49E Ch. 16.5 - 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Prob. 26CRE Ch. 16 - Prob. 27CRE Ch. 16 - Prob. 28CRE Ch. 16 - Prob. 29CRE Ch. 16 - Prob. 30CRE Ch. 16 - Prob. 31CRE Ch. 16 - Prob. 32CRE Ch. 16 - Prob. 33CRE Ch. 16 - Prob. 34CRE Ch. 16 - Prob. 35CRE Ch. 16 - Prob. 36CRE Ch. 16 - Prob. 37CRE Ch. 16 - Prob. 38CRE Ch. 16 - Prob. 39CRE Ch. 16 - Prob. 40CRE Ch. 16 - Prob. 41CRE Ch. 16 - Prob. 42CRE Ch. 16 - Prob. 43CRE Ch. 16 - Prob. 44CRE Ch. 16 - Prob. 45CRE Ch. 16 - Prob. 46CRE Ch. 16 - Prob. 47CRE Ch. 16 - Prob. 48CRE Ch. 16 - Prob. 49CRE Ch. 16 - Prob. 50CRE Ch. 16 - Prob. 51CRE Ch. 16 - Prob. 52CRE Ch. 16 - Prob. 53CRE Ch. 16 - Prob. 54CRE Ch. 16 - Prob. 55CRE Ch. 16 - Prob. 56CRE Ch. 16 - Prob. 57CRE Ch. 16 - Prob. 58CRE Ch. 16 - Prob. 59CRE Ch. 16 - Prob. 60CRE Ch. 16 - Prob. 61CRE

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The sketch of the domain of integration of ∫ 0 4 ∫ y 2 4 x 2 + 5 y d x d y and to evaluate the integration which is changed as an iterated integral in the opposite order.

Solution Summary: The author explains the sketch of the domain of integration of 0 4 y, which is sketched such that the limits correspond to the inequalities describing the following shaded horizontally simple region.

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The sketch of the domain of integration of $\int_{0}^{4} \int_{\sqrt{y}}^{2} \sqrt{4 x^{2} + 5 y} d x d y$ and to evaluate the integration which is changed as an iterated integral in the opposite order.

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Chapter 16 Solutions

The sketch of the domain of integration of ∫ 0 4 ∫ y 2 4 x 2 + 5 y d x d y and to evaluate the integration which is changed as an iterated integral in the opposite order.

Solution Summary: The author explains the sketch of the domain of integration of 0 4 y, which is sketched such that the limits correspond to the inequalities describing the following shaded horizontally simple region.

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Chapter 16 Solutions

The sketch of the domain of integration of $\int_{0}^{4} \int_{\sqrt{y}}^{2} \sqrt{4 x^{2} + 5 y} d x d y$ and to evaluate the integration which is changed as an iterated integral in the opposite order.