   Chapter 15, Problem 4RQ

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. ∫ − 1 1   ∫ 0 1 e x 2   +   y 2   sin y   d x   d y   =   0

To determine

Whether the statement, “ 1101ex2+y2sinydxdy=0 ” is true or false.

Explanation

Defition used:

If f is a continuous function and f(x)=f(x) , then f is said to be an odd function.

Formula used:

If g(x) is the function of x and h(y) is the function of y then,

abcdg(x)h(y)dydx=abg(x)dxcdh(y)dy (1)

If f is an odd function, then aaf(x)dx=0 (2)

Reason:

By the equation (1), separate the given integrals and integrate it.

1101ex2+y2sinydxdy=11ey2siny

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