   Chapter 15.2, Problem 56E

Chapter
Section
Textbook Problem

Evaluate the integral by reversing the order of integration. ∫ 0 8 ∫ y 3 2 e x 4   d x   d y

To determine

To reverse: The order of the integration and find the value of given double integral.

Explanation

Given

The function is f(x,y)=ex4 .

The domain D is, D={(x,y)|y3x2,0y8} .

Calculation:

Reverse the order of integration, D will become D={(x,y)|0x2,0yx3} . The value of the double integral is,

Df(x,y)dA=08y32ex4dxdy=020x3ex4dydx

First, compute the integral with respect to y.

020x3ex4dydx=02[0x3ex4dy]dx=02ex4[y]0x3dx

Apply the limit value for y,

020x3e

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