   Chapter 15, Problem 6RE

Chapter
Section
Textbook Problem

Calculate the iterated integral.6. ∫ 0 1 ∫ x e x 3 x y 2   d y   d x

To determine

To calculate: The value of given iterated integral.

Explanation

Calculation:

First, compute the integral with respect to y.

01xex3xy2dydx=01[xex3xy2dy]dx=01[3xy33]xexdx=01[xy3]xexdx

Apply the limit values for y,

01xex3xy2dydx=01[(x(ex)3)(x(x)3)]dx=01[(xe3x)(x4)]dx=01(xe3xx4)dx=01xe3xdx01x4dx

Compute the integral with respect to x. For that use the technique of integration by parts for the first integrand. Let u=x and dv=e3xdx . Then, du=dx and v=e3x3

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