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

Determine the area of the indicated region.Region bounded by $f(x)=3 x^{2}$ and the $x$ -axis, between $x=-1$ and $x=2$.

9

Calculus 1 / AB

Chapter 5

Integration and its Applications

Section 6

The Definite Integral

Integrals

Missouri State University

Oregon State University

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.

01:52

Determine the area of the …

02:29

03:06

01:29

01:44

02:25

14:06

Find the area of the regio…

01:45

04:20

So any time we have a area problem and we want the area bounded with the X axis, that's just saying, Hey, let's do the integral So that's that's your first clue. And they also give you other bounds, like X equals negative one and X equals two. Uh, and so those are your boundaries. So, like your lower bound and we'd like to go in order from least to greatest. Otherwise you wouldn't get a negative area, which doesn't make a lot of sense. Um, but when we look at this, then you have your function three x squared D X. So as you're looking at that, it makes perfect sense that we can just go ahead and find the anti Kuroda, which is adding one to your exponents and then divide by that new experiment. Don't forget about the three in front, though three divide by three were reduced to one. We're just going from negative 1 to 2. So now you can plug in your balance, which would be two cubed, minus negative one cube. And just as a reminder, I don't know how good you are at this, but two times two times two is eight nee one Huge. Uh, maybe one times everyone times everyone is still negative. 13 negatives is still needs. So that turns into plus eight plus one to give you an answer of nine. That's your correct answer. Night. Mhm.

View More Answers From This Book

Find Another Textbook

Numerade Educator

06:30

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

02:55

Determine the total area between the curve and the $x$ -axis shown in Fig. E…

01:57

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

01:18

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

04:04

Evaluate the given integral.$$\int \frac{(\ln x)^{N}}{x} d x$$

02:15

(a) Compute $\frac{d}{d x}\left(\frac{1}{b} \ln (a+b x)\right) ;$ use this t…

06:28

Find (a) $f_{x x}(x, y),$ (b) $f_{y y}(x, y),$ (c) $f_{x y}(x, y),$ and $f_{…

02:46

Determine $G(x)$.$$G(x)=x^{2} \int_{0}^{x} t^{3} d t$$

01:26

Evaluate the given integral.$$\int 4^{2 x} d x$$

01:17

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