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Mathematics
Mathematics
Problem
On the interval
[
−
3
,
6
]
[-3,6]
[
−
3
,
6
]
the graph of
f
f
f
consists of a semicircle of radius
3
3
3
lying above the
x
x
x
-axis on
[
−
3
,
3
]
[-3,3]
[
−
3
,
3
]
and
f
(
x
)
=
0
f(x)=0
f
(
x
)
=
0
for
3
<
x
≤
6
3<x\le6
3
<
x
≤
6
. Let
g
(
x
)
=
∫
−
3
x
f
(
t
)
d
t
.
g(x)=\int_{-3}^{x} f(t)\,dt.
g
(
x
)
=
∫
−
3
x
f
(
t
)
d
t
.
Calculate the exact value of
g
(
3
)
g(3)
g
(
3
)
.
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