Submitted by marshmallow on Tue, 04/11/2017 - 13:15
Forums:
I am stuck on part ii) and was wondering if I could have hint on the right direction to go in.
So far I have tried doing substitution of x=u-1/2 in order to get the limits similar to part i), and then was trying to do integration by parts. However I am struggling to simplify the sin(1/x) part into f(a-x).
Thank you.
Sorry- I meant:
I meant I tried u=x-1/2
This part of the question is
This part of the question is not directly related to the previous part so you don't want to try to reduce the integral to the form of $I$ in part (i). However, if I write the integral in the form $$J=\int_{1/b}^{b} \frac{g(x)}{x(g(x)+g(1/x))}\,\mathrm{d}x \quad \text{where} \quad g(x)=\sin(x),\,b=2,$$perhaps you can spot a helpful substitution that will allow you to use a similar trick that you used in evaluating $I$ in part (i).
Thank you!
I used the substitution u=1/x and it worked.
Thank you very much! :)