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Mathematics
Mathematics
Problem
Let
f
(
t
)
=
3
sin
(
2
t
)
f(t)=3\sin(2t)
f
(
t
)
=
3
sin
(
2
t
)
and define
g
(
x
)
=
∫
π
/
6
x
f
(
t
)
d
t
g(x)=\displaystyle \int_{\pi/6}^{x} f(t)\,dt
g
(
x
)
=
∫
π
/6
x
f
(
t
)
d
t
. What is the value of
g
(
π
2
)
g\!\left(\dfrac{\pi}{2}\right)
g
(
2
π
)
? a)
−
9
4
-\dfrac{9}{4}
−
4
9
b)
9
4
\dfrac{9}{4}
4
9
c)
9
2
\dfrac{9}{2}
2
9
d)
3
4
\dfrac{3}{4}
4
3
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