Question

Can you evaluate the integral by interpreting it in terms of areas?

Answer 1

Please see below.

Explanation:

`y=1/3x-2` has a graph that is a line. Sketch the line from `x=0` to `x = 9`.

The integral will be the negative of the area under the `x`-axis and above the line PLUS the area under the line and above the `x`-axis.

In the picture below, it is the negative of the red area plus the positive blue area.

If you prefer, use the blue area minus the red area.

Note that the area of a triangle is `A = 1/2bh` where `b` is the base and `h` is the height.