# average value on an interval

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• Jan 7th 2007, 03:19 PM
abcocoa
average value on an interval
please help!

The average value of cosx on the interval [-3,5] is...?

I looked in my book and asked a friend but nobody understands...the answer is supposed to be (sin3 + sin5)/8...
• Jan 7th 2007, 03:25 PM
ThePerfectHacker
Quote:

Originally Posted by abcocoa
please help!

The average value of cosx on the interval [-3,5] is...?

I looked in my book and asked a friend but nobody understands...the answer is supposed to be (sin3 + sin5)/8...

$\int_{-3}^5 \cos x=\sin x\big|_{-3}^5=\sin5-\sin(-3)=\sin 5+\sin 8$
Then divide it by the length of interval,
$5-(-3)=8$
Correct answer thou hath.
• Jan 8th 2007, 01:19 AM
topsquark
In general (assuming the integral can be done, etc.) the average (mean) value of a function f(x) over the interval (a, b) is:
$\overline{f} = \frac{1}{b - a} \int_a^b dx f(x)$

You can find this under the heading "mean value theorem for integration" or something similar.

-Dan