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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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BuyFindarrow_forward

Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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For the double integral 0 2 2 y 4 d x   d y ,

a. sketch the region R whose area is represented by the integral,

b. rewrite the integral so that x is the outer variable, and

c. show that both orders of integration yield the same value.

(a)

To determine

To graph: The region R whose area is represented by the double integral 022y4dxdy.

Explanation

Given Information:

The provided double integral is 022y4dxdy.

Graph:

Consider the double integral 022y4dxdy.

From the inner limits, it is clear that,

2yx4

The region R is bounded by the line x=2y in left side and by the line x=4 in right side

(b)

To determine

To calculate: The rearranged from of integral 022y4dxdy so that x is the outer variable.

(c)

To determine

To prove: The double integral 022y4dxdy and 040x2dydx yields the same value.

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