Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Question

Answered step-by-step

If $ \displaystyle f(x) = \int^x_0 (1 - t^2) e^{t^2} \,dt $, on what interval is $ f $ increasing?

Video Answer

Solved by verified expert

This problem has been solved!

Try Numerade free for 7 days

Like

Report

Official textbook answer

Video by Amrita Bhasin

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

00:57

Frank Lin

Calculus 1 / AB

Chapter 5

Integrals

Section 3

The Fundamental Theorem of Calculus

Integration

Campbell University

Harvey Mudd College

Idaho State University

Lectures

05:53

In mathematics, an indefinite integral is an integral whose integrand is not known in terms of elementary functions. An indefinite integral is usually encountered when integrating functions that are not elementary functions themselves.

40:35

In mathematics, integration is one of the two main operations of calculus, with its inverse operation, differentiation, being the other. Given a function of a real variable (often called "the integrand"), an antiderivative is a function whose derivative is the given function. The area under a real-valued function of a real variable is the integral of the function, provided it is defined on a closed interval around a given point. It is a basic result of calculus that an antiderivative always exists, and is equal to the original function evaluated at the upper limit of integration.

0:00

If $f(x)=\int_{0}^{x}\left…

01:21

01:05

Find the interval of the i…

10:26

$$ f(x)=\int_{0}^{x}\left(…

01:32

Statement 1 $f(x)=\int_{0}…

01:09

Suppose the derivative of …

00:50

$$\begin{array}{l}{\te…

02:19

02:05

Okay, The first thing you know is the directive one minus X squared times E to the X squared. Now we know that we have one month's ex, Corde said. Equal to zero axes, Juan or negative one cause one are negative on squared, sort of this positive one know either the export always has to be positive. Therefore, we know that when access between negative 11 the function is increasing, so it's increasing. The absolute value of axe is less than one. That's essentially this simplified form in which we can write this, otherwise it's decreasing.

View More Answers From This Book

Find Another Textbook

03:11

Courtney is building a rectangular wading pool. She wants the area of the bo…

02:57

A 10-ft chain weighs 25 lb and hangs from a ceiling. Findthe work done in li…

01:04

2x + 4 = 2(4x - 16)

06:05

A 12-ounce soda can has a height of 4.875 inches. What is its average diamet…

01:06

Nicci's sister is 7 year less than twice nicci's age, a. The same …

$1500 at 7% compounded annually for 3 years, what's the total balance?<…

find the first 5 terms of a geometric sequence that starts with -5 and has a…

01:10

Find the open interval(s) where the following function is increasing, de…

01:20

Consider the following relation.−5x+8y=0Step 2 of 2: Determi…