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
Use the properties of integrals and the result of Example 3 to evaluate $ \displaystyle \int^3_1 (2e^x - 1) \, 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 Robert Daugherty
Numerade Educator
This textbook answer is only visible when subscribed! Please subscribe to view the answer
00:46
Frank Lin
00:42
Amrita Bhasin
Calculus 1 / AB
Chapter 5
Integrals
Section 2
The Definite Integral
Integration
Missouri State University
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.
01:06
Use the properties of inte…
01:02
Use the result of Example …
01:59
Use properties of integral…
01:13
00:57
Use a change of variables …
00:50
Yeah problem. 44. They want us to evaluate using properties of integral roles. The integral 1 to 3 to eat of the X men is one given that in a previous exercise. A few pages before this they work through an example and found this result. So properties of integral is here. This is going to be the integral from 1 to 3 of two. E to the X D x minus. The integral from 1 to 3 D X. That is to times the integral from 1 to 3. Either the X D x minus. The integral from 1 to 3 D X. Now the result that you see here, I already know that value so I can substitute that in. So this is going to be yeah, two. Mhm E cubed minus E minus. And this is just going to be three minus one. So when you do that integral is going to be So 3 -1. The reason you see this is, what does that function look like? This is like, well, one if y is equal to one from 1 to 3. Yeah, so here's one, here's one, here's three. What is the area of this rectangle? That is a one by three rectangle? Excuse me? one x 1 x two Rectangle. So it turns out this is just simply two E cubed minus E -2. Or if you factor to out of everything, EQ -E -1 is the final answer there.
View More Answers From This Book
Find Another Textbook
02:10
the sum of the first 3 term of the gp is 9a while the term of the first six…
04:51
manav drives from his home to the nearest metro station at an average speed …
02:34
Statements :All hill stations have a sun-set point. X is a hill station.…
01:26
Write the role of business ethics ? Mnc with an example
05:12
Find the range of the real valued function: f(x) = log |4 - x²|
01:38
Factorise :- 7 ( x - 2y )^2 - 25 ( x - 2y ) + 12
01:50
Write the relation between weight, w of an object and its mass m.