Find the area between two curves.

  • Thread starter jumbogala
  • Start date
  • #1
423
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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!
 
Last edited:

Answers and Replies

  • #2
lanedance
Homework Helper
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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
 
  • #3
423
2
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?
 
  • #4
lanedance
Homework Helper
3,304
2
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
 
  • #5
423
2
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!
 

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