Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Given real numbers $a,b$ such that $0<a<b$ and $m=\dfrac{a+b}{2}<\dfrac{\pi}{4}$,evaluate

$$\displaystyle\lim_{\xi\to 0^{+}}\left(\displaystyle\int_{a}^{m-\xi}f(x)dx+\displaystyle\int_{m+\xi}^{b}f(x)dx\right)$$

where $$f(x)=\dfrac{(1+\cos{(2m-2x)})\cos{(a-x)}\cos{(b-x)}}{(1-\sin{(a-x)})(1-\sin{(b-x)})\sin{(2m-2x)}}$$

Thank you everyone!

share|improve this question
I would try the affine change of variable exchanging $a$ and $b$ and fixing $m$ to see how it goes. Maybe that's useless...but that's what I would do first. –  1015 Mar 28 '13 at 5:33
yes, I have do this methods, But I failed. –  math110 Mar 28 '13 at 5:41
You could try expressing %f% in terms of the exponential function. –  JacksonFitzsimmons Jun 24 at 23:26

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.