Thread: Trouble finding area between graphs

Hey guys, I'm having trouble with this problem, maybe you can help me out?

Let f (x) = 72 + x - x2 and g (x) = x2 - 9x.
Find the area between the graphs of f and g over [1, 6].

What have you tried so far?

I'd work with the formula: integral of g(x) - f(x)

I tried that brother! Except the graphs cross at 4.3245, so, from what I think I've learned haha , I split it into two parts, integrating from 0 to 4.3245 and 4.3245 to 6. f(x)-g(x) for the first part because f is higher than g, then g(x)-f(x) for the second part, because g was higher than f. Where am I going wrong?

It would help if you posted your working.

the graphs cross at 4.3245

They don't cross at 4.3245. You don't need to do 2 integrals.

Doing f(x) - g(x) seems more correct to me. f(x) should be higher.

You need to solve 72 + x - x^2= x^2 - 9x to find the points at which the graphs cross. If you integrate with respect to x, you can do it with only one integration.