   Chapter 15, Problem 2P

Chapter
Section
Textbook Problem

Evaluate the integral ∫ 0 1 ∫ 0 1 e max { x 2 ,   y 2 } d y   d x where max{x2, y2} means the larger of the numbers x2 and y2.

To determine

To evaluate: The given integral.

Explanation

Given:

The function, f(x,y)=emax{x2,y2}.

Calculation:

Since the given region is the unit length box in the first quadrant, the center diagonal line is exactly the line y=x. Separate the given region R into two parts, in which one contains the values which has max{x2,y2}=x2 and another contains the values in which max{x2,y2}=y2. So, separate the integral into two parts as shown below.

0101emax{x2,y2}dydx=010xex2dydx+010yey2dxdy

Integrate it and apply the limit.

0101emax{x2,y2}dydx=01[ex2y]0xdx+01[xey2]0ydy=01[ex2(x0)]dx+01[ey2(</

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