find average value of y = cos x from 0 to pie/2
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Answer:
The average value of the function
f
(
x
)
on the interval
[
a
,
b
]
can be evaluated through the following the following expression:
average value
=
1
b
−
a
∫
b
a
f
(
x
)
d
x
Here, this gives us an average value of:
1
π
2
−
0
∫
π
2
0
cos
(
x
)
d
x
Integrating
cos
(
x
)
gives us
sin
(
x
)
:
=
1
π
2
[
sin
(
x
)
]
π
2
0
=
2
π
[
sin
(
π
2
)
−
sin
(
0
)
]
=
2
π
[
1
−
0
]
=
2
π
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