   Chapter 15, Problem 3RE

Chapter
Section
Textbook Problem

Calculate the iterated integral.3. ∫ 1 2 ∫ 0 2 ( y   +   2 x e y )   d x   d y

To determine

To calculate: The value of given iterated integral.

Explanation

Calculation:

First, compute the integral with respect to x.

1202(y+2xey)dxdy=12[02(y+2xey)dx]dy=12[(xy+2x2ey2)]02dy

Apply the limit values for x,

1202(y+2xey)dxdy=12[(y(2)+2(2)2ey2)(y(0)+2(0)2ey2)]dy=12[(2y+4ey)(0+0)]dy=12(2y+4ey)dy

Compute the integral with respect to y

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