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the definite inegral of (ln x)^2 - 1 (part of a geometry problem)

from e^-1 to e

I tried this:

[(x ln x - x)^3]/3 - x

And got 2.48, but looking at the graph it looks like it should be about 1.5.

This is just a homework problem, but none of the class can get it.

I also have another question on a different problem.

a definite integral from -.5 to .5

SQRT[1-(2 cos (pi*x))^2]

I got as far as SQRT[1 - 4pi^2sin^2(pi*x) and I have NO idea how to integrate that.

None of the class could figure out this one either.

My calculus teacher is about 75 years old, and she shouldn't be teaching, I feel like I haven't learned anything except what I have taught myself.

Thank you for any help!