Explanation Given: Map for change of variables. x = sin u cos v , y = sin v cos u . Calculation: Let us use the new variables such that: x = sin u cos v , y = sin v cos u . Thus, we get the new integrand as: 1 1 − x 2 y 2 = 1 1 − ( sin u cos v ) 2 ( sin v cos u ) 2 = 1 1 − tan 2 u tan 2 v . Let us now evaluate the Jacobian: Jacobian = [ ∂ ( sin u cos v ) d u ∂ ( sin v cos u ) d u ∂ ( sin u cos v ) d v ∂ ( sin v cos u ) d v ] = [ ( cos u cos v ) sin v sec u tan u sin u sec v tan v ( cos v cos u ) ] Jacobian = ( cos

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ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 16.6, Problem 45E

To determine

To evaluate:

The integral $\int_{0}^{1} \int_{0}^{1} \frac{d x d y}{1 - x^{2} y^{2}}$

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Chapter 16.6, Problem 44E

Chapter 16.6, Problem 46E

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Chapter 16 Solutions

CALCULUS (CLOTH)

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The integral ∫ 0 1 ∫ 0 1 d x d y 1 − x 2 y 2

Solution Summary: The author evaluates the given integral using change of variables and its value is 1.2337.

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To evaluate:

The integral $\int_{0}^{1} \int_{0}^{1} \frac{d x d y}{1 - x^{2} y^{2}}$

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Chapter 16 Solutions

The integral ∫ 0 1 ∫ 0 1 d x d y 1 − x 2 y 2

Solution Summary: The author evaluates the given integral using change of variables and its value is 1.2337.

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Chapter 16 Solutions

To evaluate:

The integral $\int_{0}^{1} \int_{0}^{1} \frac{d x d y}{1 - x^{2} y^{2}}$