Question

Find the area between the curves y = x^2 - 9 and y = (2x-1)(x+3)
Find the area between the curves y = x^2 - 9 and y = (2x-1)(x+3)
@Mathematics

Answer 1

steps or answer?
http://www.wolframalpha.com/input/?i=area+between+the+curves+y+%3D+x^2+-+9+and+y+%3D+%282x-1%29%28x%2B3%29

Answer 2

steps please

Answer 3

ok first you have to find where they intersect to find the limits of integration, so set
\[x^2-9=(2x-1)(x+3)\] and solve the resulting quadratic equation

Answer 4

multiply out and put everything on one side of the equal sign to get
\[x^2+5x+6=0\] so
\[(x+3)(x+2)=0\] and the fore
\[x=-3,x=-2\] and those will be the lower and upper limit respectively

Answer 5

how comes the hardest part, figuring out which curve is above the other. probably the easiest thing to do is graph, or plug in some number to see which one is better. you will find that
\[x^2-9\] is above
\[2x^2+5x-3\] so you want to integrate the upper curve minus the lower one

Answer 6

\[\int_{-3}^{-2} x^2-9-(2x^2+5x-3)dx\]

Answer 7

use some algebra to simplify the integrand, take the anti derivative, plug in -2, plug in -3 and subtract