I think I'm getting the hang of evaluating integrals, but I just wanted to check my answer. Is someone able to confirm if this working and result are correct?
Let
Substituting values gives:
You are getting things mixed up and confused. When making a substitution in a definite integral, you can either:
1. Change the integral terminals and then evaluate the new definite integral: , or
2. Get the anti-derivative in terms of the new variable, re-substitute to get the anti-derivative in terms of the old variable and then evaluate the definite integral in terms of the old variable: .
You do one or the other. You're mixing both together.
The correct answer is 1/2:
1. .
2. .
NO!