Explanation Given: ∫ 0 1 ∫ 0 y sin x 1 − x d x d y Calculation: The given region is: D : 0 ≤ y ≤ 1 , 0 ≤ x ≤ y The sketch of the region is as shown in the Figure: Since x = y and y = x so the region can also be defined as: D : 0 ≤ x ≤ 1 , x ≤ y ≤ 1 Then, the integral can be rewritten as: ∫ 0 1 ∫ 0 y f ( x ) d x d y = ∫ 0 1 ∫ x 1 f ( x ) d x d y = ∫ 0 1 [ y f ( x ) ] y = x 1 d x = ∫ 0 1 ( 1 − x ) f ( x ) d x Thus, it is proved that ∫ 0 1 ...

4th Edition

ISBN: 9781319323394

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 16, Problem 21CRE

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To calculate:

The value of $\int_{0}^{1} \int_{0}^{y} \frac{\sin x}{1 - x} d x d y$ using the formula $\int_{0}^{1} \int_{0}^{y} f (x) d x d y = \int_{0}^{1} (1 - x) f (x) d x$ .

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Chapter 16, Problem 20CRE

Chapter 16, Problem 22CRE

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Chapter 16 Solutions

CALCULUS W/SAPLING ACCESS >IC<

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The value of ∫ 0 1 ∫ 0 y sin x 1 − x d x d y using the formula ∫ 0 1 ∫ 0 y f ( x ) d x d y = ∫ 0 1 ( 1 − x ) f ( x ) d x .

Solution Summary: The author explains how the integral can be rewritten using the formula 0 10 y sin x 1

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To calculate:

The value of $\int_{0}^{1} \int_{0}^{y} \frac{\sin x}{1 - x} d x d y$ using the formula $\int_{0}^{1} \int_{0}^{y} f (x) d x d y = \int_{0}^{1} (1 - x) f (x) d x$ .

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Chapter 16 Solutions

The value of ∫ 0 1 ∫ 0 y sin x 1 − x d x d y using the formula ∫ 0 1 ∫ 0 y f ( x ) d x d y = ∫ 0 1 ( 1 − x ) f ( x ) d x .

Solution Summary: The author explains how the integral can be rewritten using the formula 0 10 y sin x 1

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To calculate: The value of ∫01∫0ysinx1−xdxdy using the formula ∫01∫0yf(x)dxdy=∫01(1−x)f(x)dx.

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Chapter 16 Solutions

To calculate:

The value of $\int_{0}^{1} \int_{0}^{y} \frac{\sin x}{1 - x} d x d y$ using the formula $\int_{0}^{1} \int_{0}^{y} f (x) d x d y = \int_{0}^{1} (1 - x) f (x) d x$ .