   Chapter 5.3, Problem 64E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# If f ( x ) = ∫ 0 x ( 1 − t 2 ) e t 2   d t , on what interval is f increasing?

To determine

To find: the interval for the integral when the function f is increasing.

Explanation

Given information:

The function is f(x)=0x(1t2)et2dt.

Calculation:

Show the function as follows:

f(x)=0x(1t2)et2dt (1)

The Fundamental Theorem of Calculus, Part 1 is shown below:

g(x)=axf(t)dt axb

Here the continuous function on the interval [a,b] is f and the function is g.

Condition for the theorem to be valid:

• If the function is continuous on the interval [a,b] and differentiable on (a,b)

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