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

Evaluate the integral.

$ \displaystyle \int^5_{-5} e \,dx $

Video Answer

Solved by verified expert

This problem has been solved!

Try Numerade free for 7 days

Like

Report

Official textbook answer

Video by Yuki Hotta

Numerade Educator

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

00:46

Frank Lin

00:17

Amrita Bhasin

Calculus 1 / AB

Chapter 5

Integrals

Section 3

The Fundamental Theorem of Calculus

Integration

Oregon State University

Harvey Mudd College

University of Nottingham

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.

00:26

Evaluate the integral.…

03:15

03:13

01:10

Evaluate the given integra…

01:27

01:55

Evaluate the integrals.

03:09

01:00

Find the indefinite integr…

Okay, now we're going to answer the question. The integral off negative 5 to 5 e d. X Evaluate this thing. Okay, this is actually a trick question. A lot of people will associate E with the exponential function E to the X. Who's derivative is going to be e to the X and the integral is also a family of E to the X. Let's just not forget that are constant also comes into play. However, this is not a net exponential function. It doesn't have any X in the power. This is just eat. So it's almost the same as saying Find the integral off three approximately or 2.718 if you remember what this constant is approximately equal to. So this is simply a polynomial, a constant polynomial. So if you take the anti derivative, it'll be e times x, not eat to the X, okay, and then we can plug in negative 5 to 5. Of course, this is just a rectangle with height e where the base is going to be length 10 because that's a distance from negative 5 to 5. The answer is 10 e. So please do not fall for the job for this problem

View More Answers From This Book

Find Another Textbook

01:19

You can make concrete by mixing 1part cement with 2 parts pea gravel and 3 p…

00:44

using the same ratios, how much cement and how much pea gravel should you us…

12:02

Studies are often done by pharmaceutical companies to determine the effectiv…

Write the logarithmic equation log7x = y in exponential form.

02:35

Annie is concerned over a report that "a woman over age 40 has a better…

02:01

01:39

Postpartum depression and anxiety (PPD), is a common medical condition affec…

01:58

A famous designer gave away free perfume samples in the mall, and in 15 minu…

02:36

Solve the given problem.If x<0, is it ever true that X^-2 < x^-1?…