Math Is Fun Forum

da_coolest

Member

Registered: 2009-05-12

Posts: 1

How to find the area enclosed by two curves?

f(x) = 2x - x²

g(x) = 3 - 2x²

how do i find the area enclosed by two graphs?

thanks in advance!

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: How to find the area enclosed by two curves?

da_coolest, find the intersection points, this is the area you want to be calculating.  Now over this area, you want to calculate the integral of f(x) - g(x), or alternatively g(x) - f(x), which ever is positive.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: How to find the area enclosed by two curves?

When doing this sort of problem, always try and sketch the graphs. Then you can see more clearly what the problem involves.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: How to find the area enclosed by two curves?

How true and in the spirit of Acton. People involved in maths today hardly ever sketch a function. They immediately run to the blackboard and start thrashing and flailing around, just slinging symbols. They don't even bother with all the excellent graphing software that makes this so painless.

Last edited by bobbym (2009-05-13 11:23:33)

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.