Find the area between two curves.

[jumbogala]

Homework Statement

Find the area between the curves y= (7-x)/5, y = +sqrt(x+7) , y = -sqrt(x+7)

Homework Equations

The Attempt at a Solution

I found the points of intersection of the graphs are at x=-7, x=-3 and x=42. So I know I need to do two integrals:

One from -7 to -3, and the other from -3 to 42. But I don't know what exactly to integrate =/

Please help!

 

[lanedance]

Hi jumbogala, you're on the right track - try drawing a picture of you curves

the integral for each section will be the difference of 2 curves (greater y - lesser y valued curve)

use you picture to pick the 2 curves to use for each intergal

 

[jumbogala]

Hmm, except that there are three curves so there's actually one on top with 2 underneath... do I have to pick just 2 curves for each integral?

 

[lanedance]

if you sketch you curves, you will see all 3 bound a single area, the area you are trying to find

for any given infintesimal x interval dx, only 2 curves will be acting as the bounds, so use your curve sketch to pick the correct curves for the integral

 

[jumbogala]

okay I think I kind of get it...

Between -7 and -3 the area is bounded by +sqrt(x+7) and -sqrt(x+7)

Between -3 and 42 it is bounded by (x-7)/5 and -sqrt(x+7)

Which works, so it must be the right answer. Thank you!