Download the App!

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

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

Sketch the area represented by the given definite integral.$$\int_{-1}^{1} e^{x} d x$$

Calculus 1 / AB

Chapter 5

Integration and its Applications

Section 6

The Definite Integral

Integrals

Oregon State University

Harvey Mudd College

Baylor University

University of Nottingham

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.

01:24

Sketch the area represente…

00:58

Sketch the area correspond…

00:55

01:48

02:08

00:46

Sketch the integrand of th…

01:28

Sketch the region of integ…

01:30

01:52

01:00

01:38

Sketch the region whose ar…

01:02

Okay, so we're looking at E to the X power into the X power, and we have the integral from negative 1 to 1. So if we were to first of all, wrapped into the ex that's exactly what this is saying is we are graphing fee to the X. Uh, and I expect my students know that every exponential function without any shifts or transformation go through the order Pairs 01 Uh, this is exponential growth that was up into the right and down until left. And there's a horizontal listen to it at like 10 It's the X axis. So what you need to recognize in this problem is that X equals negative. One is a bound and Mexico is positive. One is the upper back. And what you're technically doing is you're finding the area smashed between those two values. Um, yeah. Mhm, Yeah, that's that's what this problem is asking you for. Um, I don't know if it needs any more specific values like the Y value here would be e to the negative first power because you're plugging in that bound or either the first power. But you can evaluate the problem this way and understand that this is your graph of that visual

View More Answers From This Book

Find Another Textbook

Solve the given differential equation.$$\frac{d y}{d x}=\frac{2 x^{3}}{y…

01:59

(a) determine a definite integral that will determine the area of the region…

01:09

Determine the region $R$ determined by the given double integral.$$\int_…

02:52

Use the method of Lagrange multipliers to optimize $f$ as indicated, subject…

03:25

Show that the mixed second derivatives for the Cobb-Douglas Production funct…

02:01

A function is said to be homogeneous of degree $n$ if $f(\gamma x, \gamma y)…

02:20

Sketch the area represented by the given definite integral.Integral in E…

05:22

For $f(x, y, z)=4 x^{3} y^{2} z^{2}+4 x^{2}+2 y^{3}+5 z^{5}+3 x-2 y+11 z+12$…

04:20

Determine the area of the indicated region.Region bounded between $f(x)=…

Determine the area of the indicated region.Region bounded by $f(x)=3 e^{…