Another question, but this time into this sub-forum. So I'm studying for IB finals and I'm stuck with this question:

a. Given that a>1, use the substitution u=1/x to show that

integral(1-->a)[1/(1+x^2)]dx=integral(1/a-->1)[1/(1+u^2)]

I'm able to simplify the expression to: arctan a - arctan 1 = arctan 1 - arctan a. Should I do it this way or is there some other way to do it and how do I get it to actually equal to each other do I have to use the information that a>1?

b. Hence show that arctan a + arctan 1/a = pi/2

So I see that arctan 1 = pi/4 right? So that would be okay (add both sides you get pi/2), but since I have to use the substitution arctan for the RHS will also be arctan a instead of arctan 1/a (it's a definite integral) so is there something I should do?

Thanks in advance.