Question

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

Answer 1

The area is `4(3 + pi)` square units.

Explanation:

This is a semicircle of radius `4` that has been moved `3` units up. The graph will be like this:

We want to find the area of the region enclosed by the four colours. This is clearly a rectangle topped by a quarter circle.

Hence the area is

`A = 4 * 3 + 1/4(4)^2pi = 12 + 4pi = 4(3 + pi)`

Hopefully this helps!