# average value on an interval

• January 7th 2007, 04:19 PM
abcocoa
average value on an interval

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...
• January 7th 2007, 04:25 PM
ThePerfectHacker
Quote:

Originally Posted by abcocoa

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,
$5-(-3)=8$
$\overline{f} = \frac{1}{b - a} \int_a^b dx f(x)$