Question

What is the net area between `f(x)=(x-3)e^x` in `x in[1,2]` and the x-axis?

Answer 1

`2e^2 - 3e`

Explanation:

Area should always be positive.

Since `f(x) < 0` for all `x in [1,2]`, the area is given by

`int_1^2 |f(x)| "d"x = int_1^2 -f(x) "d"x`

`= int_1^2 (3-x)e^x "d"x`

`= [(4-x)e^x]_1^2`

`= 2e^2 - 3e`