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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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True or False? In Exercises 59 and 60, determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.

0 1 0 x f ( x , y ) d y d x = 0 1 0 y f ( x , y ) d x d y

To determine

Whether the statement, “010xf(x,y) dy dx=010yf(x,y) dx dy” is true or false. Also, provide better explanation in case of false.

Explanation

Consider the statement,

010xf(x,y) dy dx=010yf(x,y) dx dy

First consider the expression 010xf(x,y) dy dx which is on the left side.

From the limits of integration, the inner limit of integration is xy0, which implies that the region R is bounded on the left by the line y=x and on the right by the line x=1.

Also, since 0x1, the region lies above the x-axis.

Now, consider the expression 010yf(x,y) dx dy which is on the right side

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