Question

on the interval (8, 24), the graph is a semi - circle. since the semi - circle is below the x - axis, then $\int_{8}^{24}g(x)dx$ is the negative of the area of this semi - circle. the radius of this semi - circle is $r = $. (give the numeric value.)

Explanation:

Step1: Calculate the diameter of the semi - circle

The diameter \(d\) of the semi - circle is the length of the interval \([8,24]\). Using the formula \(d = b - a\) (where \(b = 24\) and \(a = 8\)), we have \(d=24 - 8=16\).

Step2: Calculate the radius of the semi - circle

The radius \(r\) of a circle is related to the diameter by the formula \(r=\frac{d}{2}\). Substituting \(d = 16\) into the formula, we get \(r=\frac{16}{2}=8\).

Answer:

\(8\)