Chapter 14.1, Problem 44E

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

Chapter
Section

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
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, âˆ«04âˆ«y2f(x,y)dxdy.

Graph:

Take the provided iterated integral into consideration.

âˆ«04âˆ«y2f(x,y)dxdy

In the above integral, limit of x is yâ‰¤xâ‰¤2 and limit of y is 0â‰¤yâ‰¤4.

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 xâ‰¤2 and xâ‰¥y as shown in the following diagram:

Step 2: Draw the graph of inequality yâ‰¥0 and yâ‰¤4 as shown in the following diagram:

Step 3: Merge the above two graphs to sketch the area calculated by the expression âˆ«04âˆ«y2f(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