Refer a friend and earn $50 when they subscribe to an annual planRefer Now

Get the answer to your homework problem.

Try Numerade Free for 30 Days

Like

Report

Find the areas bounded by the indicated curves.$$y=x^{2}+2 x-8, y=x+4$$

Calculus 2 / BC

Chapter 26

Applications of Integration

Section 2

Areas by Integration

Missouri State University

Campbell University

Oregon State University

University of Michigan - Ann Arbor

Lectures

01:11

In mathematics, integratio…

06:55

In grammar, determiners ar…

02:56

Find the areas of the regi…

02:40

07:47

03:27

03:08

02:19

02:12

06:42

03:15

08:47

we want to find the area bounded by the curves, Y equals x squared plus two x minus eight and y equals X plus four. To solve this, we're gonna use an application of integration known as area between two curves. The appropriate definition states that the area between two curves, Y tu minus Y. One for vertical components is a equals integral A to B Y tu minus 1 20 X. If instead the curves are represented by X two minus x one. Equivalently the area is the horizontal components and you will see the D X two minus x one B Y. Thus, if we sketch this out we can identify the relative curves and bounced integrate on. So we have our integral given here are area shaded in yellow. Thus we see that from our intercepts of these two functions negative four and three. We're gonna integrate X plus four minus x squared plus two, x minus eight. Thus we have integral from negative three x plus two x minus eight minus x minus four is absolute value expert expert cuba over three plus, expert over two minus 12 X 20 to 43 or 343 over six. And our final solution note that I took the absolute value of these functions because of the fact that we need the area to be positive.

View More Answers From This Book

Find Another Textbook

In mathematics, integration is one of the two main operations in calculus, w…

In grammar, determiners are a class of words that are used in front of nouns…

Find the areas of the regions enclosed by the lines and curves.$$y=x…

Find the areas of the regions enclosed by the lines and curves.$$y=x^{4}…

Find the areas of the regions enclosed by the lines and curves.$$y=\…

Find the areas of the regions enclosed by the curves.$$x+y^{2}=3 \qu…

Find the areas of the regions enclosed by the curves.$$x+y^{2}=3 \text {…

Find the areas of the regions enclosed by the lines and curves.$$y=x^{2}…

Find the areas of the regions enclosed by the curves.$$x+4 y^{2}=4 \…

Find the areas of the regions enclosed by the curves.$$x+4 y^{2}=4 \quad…

Find the areas of the regions enclosed by the curves.$$4 x^{2}+y=4 \…

92% of Numerade students report better grades.

Try Numerade Free for 30 Days. You can cancel at any time.

Annual

0.00/mo 0.00/mo

Billed annually at 0.00/yr after free trial

Monthly

0.00/mo

Billed monthly at 0.00/mo after free trial

Earn better grades with our study tools:

Textbooks

Video lessons matched directly to the problems in your textbooks.

Ask a Question

Can't find a question? Ask our 30,000+ educators for help.

Courses

Watch full-length courses, covering key principles and concepts.

AI Tutor

Receive weekly guidance from the world’s first A.I. Tutor, Ace.

30 day free trial, then pay 0.00/month

30 day free trial, then pay 0.00/year

You can cancel anytime

OR PAY WITH

Your subscription has started!

The number 2 is also the smallest & first prime number (since every other even number is divisible by two).

If you write pi (to the first two decimal places of 3.14) backwards, in big, block letters it actually reads "PIE".

Receive weekly guidance from the world's first A.I. Tutor, Ace.

Mount Everest weighs an estimated 357 trillion pounds

Snapshot a problem with the Numerade app, and we'll give you the video solution.

A cheetah can run up to 76 miles per hour, and can go from 0 to 60 miles per hour in less than three seconds.

Back in a jiffy? You'd better be fast! A "jiffy" is an actual length of time, equal to about 1/100th of a second.