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 region whose area is given by Exercise 29.

Region bounded by $y=5 x^{3}, y=0, x=1$ and $x=2$

Calculus 1 / AB

Chapter 5

Integration and its Applications

Section 5

Sigma Notation and Areas

Integrals

Oregon State University

Baylor University

University of Michigan - Ann Arbor

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.

02:34

Find the area of the tripl…

00:21

Find the area of the shade…

00:29

In Exercises 27-30, determ…

and this problem. We're finding the area on the dartboard that I colored in in blue. It's where our is 3 to 33 and 3/4 toe. Articles four and theta is from nine. Pi over 20. Thio 11 powers 20. Okay, sort of Find the area. You need to do the double in a girl of Juan. Our DRD fada are is going from three and 3/4 which is 15. Force 24 and theta nine pi over 22 11 pi over 20. All right. The integral of our is r squared over two. So now we have nine pi over 20 11 pi over 20 R squared over two from 15. Force toe four. Do you data Mhm. Uh huh. Okay, so we plugged those in. I'm just gonna put the one half out in the front here. Hopes in a girl 16 minus 2. 25/16. Well, d theta. And then you integrate with respect to data and you just get data, um, 16 times 16 uh, 248 off. 248 16 36 412 56 2 56 minus 2. 25. Over 16. Then when you integrate with respect to theta, you get data from 11 pi over 22 99 pi over 20,000 backwards anyway. 11 pi over 20 minus nine pi over 20. Okay, so you end up with one half times 31/16 times two pi over 20 and the twos canceled and you get 31 pi over 320.

View More Answers From This Book

Find Another Textbook

02:21

Evaluate the given integral.$$\int_{2}^{3} \int_{2 y}^{y^{2}}\left(x^{2}…

13:36

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

01:44

Evaluate the given integral and check your answer.$$\int\left(t^{2}+1\ri…

01:42

Evaluate the given integral and check your answer.$$\int \frac{1}{\sqrt{…

03:40

For $f(x, y, z)=2 x^{2}-16 x+3 y^{2}-24 y+4 z^{2}-40 z+25,$ find the point(s…

01:54

Represent the given sum (which represents a partition over the indicated int…

02:46

Use the properties about odd and even functions to evaluate the given integr…

03:53

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

03:34

01:43

$f(x, y)=10 e^{x^{2}-y^{2}},$ determine (a) $f(1,1),$ (b) $f(x, x),$ (c) $f(…