Hello, Gracy!

Graph of consists of line segments and semicircles.

Use it to geometrically evaluate the following integrals.

Code:

* *
* *
* 9π/2 *
* *
*-------------*
| | *
| 12 | *
| | 2 * 10 14
--+------+------+-------*-------+---------+
0 6 8 * -2 | |
* | -8 |
* | |
*---------*
* -2π *
* *
* *

At the far left, there is a semicircle of radius 3.

. . Its area is: .

Below it is a 6-by-2 rectangle; its area is

There are two isoceles right triangles, each with area

At the far left, there is a semicircle of radius 2.

. . Its area is: .

Above it is a 4-by-2 rectangle; its area is

The regions below the x-axis have "negative areas".