# Having trouble with finding the area between curves by integration

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• Mar 13th 2014, 08:03 PM
KevinShaughnessy
Having trouble with finding the area between curves by integration
Hi,

I'm having quite a bit of trouble with this, I understand the process of finding the area but I'm having difficulty determining the actual area I need to solve for on the graph when there are more than 2 functions. Do I find the area enclosed by all 3+ functions or all the area enclosed by all the functions?

Thanks!
• Mar 13th 2014, 11:16 PM
Prove It
Re: Having trouble with finding the area between curves by integration
It depends on your problem... Which is?
• Mar 14th 2014, 12:16 AM
hollywood
Re: Having trouble with finding the area between curves by integration
Usually when you graph the functions (assuming you've done it correctly), it becomes obvious what area they're talking about. So if you can give us an example, we can probably help you. Most people have difficulty setting up the integration.

- Hollywood
• Mar 14th 2014, 07:10 AM
KevinShaughnessy
Re: Having trouble with finding the area between curves by integration
The question I was most recently stuck on is

x + 2y = 0

y = x^2

y = x + 6
• Mar 14th 2014, 07:57 AM
Shakarri
Re: Having trouble with finding the area between curves by integration
First find the points where the lines cross by finding the values of x and y that satisfy any pair of equations.

Then sketching the functions you can see which of these points are the ones you are interested in.

Attachment 30411

I suppose you are interested in the bounded area on the left side where all 3 functions form the bounds. You can discard the point on the right where the pink and grey lines cross.

Considering the 3 points of intersection first integrate between the grey and blue functions from the first point to the second point to get the shaded area in the image below
Attachment 30412

Then integrate between the pink and blue lines from the second point to the third point to get the shaded area in the image below
Attachment 30413
• Mar 15th 2014, 01:54 PM
KevinShaughnessy
Re: Having trouble with finding the area between curves by integration
Quote:

Originally Posted by Shakarri
First find the points where the lines cross by finding the values of x and y that satisfy any pair of equations.

Then sketching the functions you can see which of these points are the ones you are interested in.

...

Thanks for the reply. So the area you have to solve for has vertices that are the points of intersection of all of the functions?
• Mar 15th 2014, 02:30 PM
Shakarri
Re: Having trouble with finding the area between curves by integration
Yes that is correct