Calculus

Find the average value of the function on the given interval:

f(x)=cos(16x), [0,pi/2]

The answer I got is 1.

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2. 👎 0
3. 👁 75
1. That cannot be the correct value because the cos 16x function undergoes 4 complete oscillations from 0 to pi/2. The average value must be zero.

The indefinite integral is (1/16)sin(16x).

Evaluate it at x = pi/2 and 0 and take the difference.

0 - 0 = 0

Divide by the interval (pi/2) and you still get zero for the average value.

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2. 👎 0
posted by drwls
2. I got that the first time, but I though something was wrong.

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2. 👎 0
posted by <3
3. This is a problem that could have been answered by inspection. You have an integer number of oscillations about a mean value of zero.

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2. 👎 0
posted by drwls

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