Mathematics

Problem

For

0\le t\le 6

the graph of

y=f(t)

is the upper semicircle of radius

3

centered at

(3,0)

. The function

g

is defined by

g(x)=\displaystyle\int_{0}^{x} f(t)\,dt

for

0\le x\le 6

. What is

g(6)

? a)

9\pi

\dfrac{9\pi}{2}

\dfrac{9\pi}{4}

\dfrac{9}{2}