The total area enclosed by the graphs of

Question

y=10x^2–x^3+x
y=x^2+19x

This is a really long problem I keep getting the answer of 20.25 but it is incorrect I don't know where I am going wrong?

Answer 1

Did you get the correct intersections of the two curves?
I had them intersect at x = 0, 3, and 6

between 0 and 3 the parabola is above the curve, so the height is
x^2 + 19x - (10x^2 - x^3 + x) = x^3 - 9x^2 + 18x
between 3 and 6 the cubic lies above the parabola and its height is
-x^3 + 9x^2 - 18x

So you have to take two integrals.
Try it again.

Answer 2

Thanks I see where I made the mistake Thank you!