Problems computing area with integrals.

[haydn]

Homework Statement

Find the total area enclosed by the graphs of

y=9x^2–x^3+x
y=x^2+16x

Homework Equations

No real equations, just using integrals

The Attempt at a Solution

I graph the functions and find they intersect at 0 and 5, and that y=x^2+16x seems to be the upper function while y=9x^2-x^3+x is the lower function.

I set up an integral with the lower limit 0 and the upper limit 5, and x^2+16x - (9x^2-x^3+x) dx inside the integral.

I solve by simplifying and using the fundamental theorem of calculus and get 10.416. The homework website I'm using is telling me this is wrong...

Thank you.

 

[Dick]

They intersect at three points, not two. One is a cubic equation. Can you find them?

 

[e(ho0n3]

I've checked it which sage and I get 10.416... I say forget what the website says.

 

[e(ho0n3]

Nevermind. Follow Dick's advice.

 

[haydn]

They intersect at three points, not two. One is a cubic equation. Can you find them?

Found it and got the correct answer. Thanks a bunch!