   Chapter 4.P, Problem 7P

Chapter
Section
Textbook Problem

# Find the interval [a, b] for which the value of the integral ∫ a b ( 2 + x − x 2 )   d x is a maximum.

To determine

To find:

The interval a, b for which the given integral is a maximum

Explanation

1) Given:

ab2+x-x2dx

2) Calculation:

Graph of 2+x-x2

So, the graph of the given integral is a downward parabola. The integral is the net area between the curve and the x-axis.

The maximum value of the integral is over the interval between the zeros of the parabola because only there the area is positive.

So, find out the roots of the parabola

### 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

#### Expand each expression in Exercises 122. (x2+x1)(2x+4)

Finite Mathematics and Applied Calculus (MindTap Course List)

#### What are the domain and range of the function f with the following graph?

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

#### Evaluate the integral. 11. 01/214x2dx

Single Variable Calculus: Early Transcendentals

#### In Exercises 1-8, determine which of the matrices are regular. 

Finite Mathematics for the Managerial, Life, and Social Sciences

#### What rationalizing substitution should be made for 1x+x5dx? a) u = x b) u=x c) u=x5 d) u=x10

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