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 \int^8_2 f(x) \, dx = 7.3 $ and $ \displaystyle \int^4_2 f(x) \, dx = 5.9 $, find $ \displaystyle \int^8_4 f(x) \, 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 Stephen Hobbs

Numerade Educator

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

00:32

Frank Lin

00:36

Amrita Bhasin

Calculus 1 / AB

Chapter 5

Integrals

Section 2

The Definite Integral

Integration

Campbell University

Oregon State University

Harvey Mudd College

University of Michigan - Ann Arbor

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

$$\text { If } \int_{2…

01:08

Suppose f(x)dx = 2, f(x)dx…

02:33

If $f(x)$ is even and $\in…

00:30

Suppose that $\int_{4}^{8}…

01:59

Suppose that $\int_{7}^{-2…

02:13

If $\int_{0}^{4} f\left(\f…

02:56

Find $\int_{2}^{5} f(x) d …

01:43

If $\int_{0}^{2} f(x-3) d …

00:45

Evaluate the integral.

04:07

Suppose that $\int_{6}^{8}…

00:37

Suppose that $\int_{1}^{3}…

00:24

Suppose that $\int_{9}^{4}…

02:05

Evaluate the definite inte…

given that we have the whole area of the integral from 2 to 8, and that is 7.3. Let's go ahead and just sketch that out here. I just drew an arbitrary graph, so this is not exactly what it looks like. Of course I'm just using this as an example. But that tells us that the area here under the curve would all be 7.3. And then we're told from 2 to 4 that the area is 5.9. So then this area here would be 5.9. The question is, what is the area than from 4 to 8. So this area here, what would that evaluate too? And to do that, we could simply subtract the total area 7.3 minus 7.3 and then minus our 5.9. And that will end up giving us just go ahead and do that out. Six. That was before and 1.4. Therefore, the missing area here must be 1.4. Because if we were to add that area 1.4 plus 5.9, that would then get us back to 7.3 as well. So that is what the missing area for the integral from 4 to 8 would have to be here.

View More Answers From This Book

Find Another Textbook

04:22

A rancher wants to fence in a rectangular area of 235224 square feet and the…

01:52

A bacterial cell has a spherical shape. If the volume of thecell is increasi…

05:42

Find the points on the ellipse x^2 + 4y^2 = 4 that are farthest away from th…

05:06

A vending machine has capacity to carry 500 cans of soda. At aprice of $0.50…