therefore,
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.
I really seem to be in need of some serious revision, because I don't understand why the integral get's a minus in front of it and then the limits are 1 to 1/a, and I'm not sure I understand why you add du/u^2 at the end (namely the u^2 in the denominator)?
This seems like something that's never been taught to us, or in some respect it makes some kind of sense, but what constitutes the minus? I guess I shouldn't have posted in the university math section, but this is what you get when they give this kind of questions to you in IB finals :P