   Chapter 14.1, Problem 44E

Chapter
Section
Textbook Problem

Changing the Order of Integration In Exercises 45-50. sketch the region R of integration and change the order of integration. ∫ 0 4 ∫ y 2 f ( x , y )   d x   d y

To determine

To graph: The region R for the given iterated integral 04y2f(x,y)dxdy. Further, change the order of integration.

Explanation

Given:

The iterated integral, 04y2f(x,y)dxdy.

Graph:

Take the provided iterated integral into consideration.

04y2f(x,y)dxdy

In the above integral, limit of x is yx2 and limit of y is 0y4.

To plot the equation x=y, i.e., y=x2, make a table as follows:

 x 0 1 2 y 0 1 4

Step 1: Sketch the graph of inequality x2 and xy as shown in the following diagram:

Step 2: Draw the graph of inequality y0 and y4 as shown in the following diagram:

Step 3: Merge the above two graphs to sketch the area calculated by the expression 04y2f(x,y)dxdy, as follows:

Interpretation:

From the graph, it can be seen that there are two limits present, that means the outside and inside limits

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

Find more solutions based on key concepts 