   Chapter 15, Problem 20RE

Chapter
Section
Textbook Problem

Calculate the iterated integral by first reversing the order of integration. ∫ 0 1 ∫ y 1 y e x 2 x 3   d x   d y

To determine

To calculate: The iterated integral by reversing the order of integration.

Explanation

Given:

The iterated integral is 01y1yex2x3dxdy .

Calculation:

Since x is varying between 0 and 1 and y varies between y and 1, the region lies between the line x=1 and the piece of parabola y=x2 and. From this, it is concluded that the sides of the given region are y=x2 , x=1 and y=0 . Thus, the limits of x and y can also be intimated as follows. x varies from 0 to 1 and y varies from 0 to x2 . Then, the given iterated integral becomes,

01y1yex2x3dxdy=010x2yex2x3dydx

First, compute the integral with respect to y.

010x2yex2x3dydx=01[0x2yex2x3dy]dx=01[y2ex22x3]0x2dx

Apply the limit values for y,

010x2yex2x3dydx=01[(

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Describe the scores in a sample that has standard deviation of zero.

Statistics for The Behavioral Sciences (MindTap Course List)

Draw the graph of each equation: x=6

Elementary Technical Mathematics

19.

Mathematical Applications for the Management, Life, and Social Sciences

If f(x) 5 for all x [2, 6] then 26f(x)dx. (Choose the best answer.) a) 4 b) 5 c) 20 d) 30

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 