# How to find the area enclosed by two curves?

• May 12th 2009, 12:46 PM
da_coolest
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?

• May 12th 2009, 12:49 PM
e^(i*pi)
Quote:

Originally Posted by da_coolest
f(x) = 2x - x²

g(x) = 3 - 2x²

how do i find the area enclosed by two graphs?

$\int ^a_b f(x) - \int ^a_b g(x)$

the limits are the points where the two lines intersect

In this case:

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

Solve the quadratic to give x = 1, -3

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

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