   Chapter 15, Problem 6RQ

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 4   ∫ 0 1 ( x 2   +   y )   sin ( x 2   y 2 ) d x   d y   ≤   9

To determine

Whether the statement, “ 1401(x2+y)sin(x2y2)dxdy9 ” is true or false.

Explanation

Formula used:

If g(x) is the function of x , g(x)M and A(R) is the area of the given region R, then, Rf(x,y)dydxM.A(R) (1)

Reason:

In the given statement, it is understood that x can take the value at most 1 and y can take the value at most 4. Sin value cannot exceed 1. Put x=1,y=4 in the given statement. Then, the function can take the value at most 3 as given below.

(x2+y)sin(x2y2)(12+4)sin(x2y2

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