   Chapter 15, Problem 2RQ

Chapter
Section
Textbook Problem

Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement. ∫ 0 1   ∫ 0 x x   +   y 2     d y   d x   =     ∫ 0 x   ∫ 0 1 x   +   y 2     d x   d y

To determine

Whether the statement, “ 010xx+y2dydx=0x01x+y2dxdy ” is true or false.

Explanation

Definition used:

Region of type 1:

A plane region D is said to be of type 1 if it lies between two continuous functions of x.

That is, D={(x,y)|axb,g1(x)yg2(x)} , where g1(x) and g2(x) are the continuous functions of x.

Region of type 2:

A plane region D is said to be of type 2 if it lies between two continuous functions of y.

That is, D={(x,y)|ayb,h1(y)xh2(y)} , where h1(y) and h2(y) are the continuous functions of y

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