Question

What is the area under the curve in the interval [-3, 3] for the function `f(x)=x^3-9x^2`?

Answer 1

I found `162` units of area.

Explanation:

Consider the area (in orange):

You get:
`Area=int_-3^3(x^3-9x^2)dx=[x^4/4-cancel(9)^3x^3/cancel(3)]_-3^3=-243/4-405/4=-162`
Negative as below the `x` axis.