# Calculus

• February 22nd 2006, 12:42 PM
frozenflames
Calculus
The average value of cos x on the interval [–3, 5] is

A) (sin 5 – sin 3)/8

B) (sin 5 – sin 3)/2

C) (sin 3 – sin 5)/2

D) (sin 3 + sin 5)/2

E) (sin 3 + sin 5)/8
• February 22nd 2006, 02:16 PM
ThePerfectHacker
Quote:

Originally Posted by frozenflames
The average value of cos x on the interval [–3, 5] is

A) (sin 5 – sin 3)/8

B) (sin 5 – sin 3)/2

C) (sin 3 – sin 5)/2

D) (sin 3 + sin 5)/2

E) (sin 3 + sin 5)/8

First find the definite integral,
$\int^5_3\cos xdx$
Which is by the fundamental theorem,
$\sin 5+\sin 3$
Now divide by the length of the interval which is,
$5-(-3)=8$
Thus, the answer is,
$(\sin 5+\sin 3)/8$