Average Values
a. Verify that ∫ln x dx = x ln x - x + C.
b. Find the average value of ln x over [1, e].
Step 1:
In this question, we have to verify the given indefinite integral and find the average value of over
.
Step 2:
(a) The given indefinite integral is .
. Now integrating by parts taking
as the first function,
The integral is verified.