f(x) = 2x - x²
g(x) = 3 - 2x²
how do i find the area enclosed by two graphs?
thanks in advance!
$\displaystyle \int ^a_b f(x) - \int ^a_b g(x)$
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