f(x) = 2x - x²

g(x) = 3 - 2x²

how do i find the area enclosed by two graphs?

thanks in advance!

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- May 12th 2009, 12:46 PMda_coolestHow 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! - May 12th 2009, 12:49 PMe^(i*pi)
$\displaystyle \int ^a_b f(x) - \int ^a_b g(x)$

the limits are the points where the two lines intersect

In this case:

$\displaystyle 2x-x^2 = 3-2x^2 \: , \: x^2+2x-3=0$

Solve the quadratic to give x = 1, -3

$\displaystyle \int ^1_{-3} (2x-x^2)dx - \int ^1_{-3} (3-2x^2) dx$

If your answer is negative then ignore the minus sign/take the absolute value - it just means you took the smaller curve from the higher one