Find the average value of the function on the indicated interval.
g(t) = cos t on
The average value is
The constant in front of the integral simplifies:
so we can write the average value as
Now to evaluate the integral, making sure we keep track of the along the way.
f(x) = 2x + 5 on [1,4]
f(x) = ex on [0,1]
For this average value, the constant out front just happens to be 1.
s(t) = 7t ln 7 on [1,3]
Since the interval length is 2, the constant in front of the integral is .
Make it rain.