   Chapter 14.1, Problem 9E

Chapter
Section
Textbook Problem

Evaluating an Integral In Exercises 3-10, evaluate the integral. ∫ 0 x 3 y e − y ▭ x d y

To determine

To calculate: The value of integral 0x3yeyxdy.

Explanation

Given:

The integral is 0x2yeyxdy.

Formula used:

Use the following rule of integration:

exdx=ex+C

Where; C is integration constant.

Use integration by parts:

f(x)g(x)dx=f(x)g(x)dx[ddx(f(x))g(x)dx]dx

Calculation:

Here, in the question, the integration is performed with respect to y, so the variable x is treated to be constant.

Now,

0x3yeyxdy=[yeyxdy(ddy(y)eyxdy)dy]0x3=[y(xeyx)(xeyx)dy

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