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Mathematics
Mathematics
Problem
Consider the function
f
(
x
)
=
sin
x
f(x)=\sin x
f
(
x
)
=
sin
x
defined on the interval
[
0
,
π
]
[0,\pi]
[
0
,
π
]
. a. (i) Find the average value of
f
f
f
on
[
0
,
π
]
[0,\pi]
[
0
,
π
]
. b. (ii) Define
g
(
x
)
=
3
sin
(
2
x
−
π
2
)
+
4
g(x)=3\sin(2x-\tfrac{\pi}{2})+4
g
(
x
)
=
3
sin
(
2
x
−
2
π
)
+
4
. Determine the average value of
g
g
g
on the interval
[
π
4
,
3
π
4
]
\bigl[\tfrac{\pi}{4},\,\tfrac{3\pi}{4}\bigr]
[
4
π
,
4
3
π
]
.
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