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.

$$ \int_0^{\pi/2}\int_{x}^{\pi/2} \frac{cos{y}} y\, dy ~dx$$

I'm not sure how to go about integrating this. I think that I need to integrate with respect to y first because the lower bound is x, which would be used for the integration with respect to x.

But, I don't know how to go about integrating the function with respect to y. How can this be done?

share|improve this question
5  
Change the limits, and integrate w.r.t. $x$ first. –  i707107 Apr 2 '13 at 8:33
    
Won't that just give me a constant multiplied by the function itself to integrate? –  bubblyicecream Apr 2 '13 at 8:50
1  
It will change your bounds and not be 'just a constant.' –  mixedmath Apr 2 '13 at 8:52
1  
Possible duplicate: Help with some double integral –  M. Strochyk Apr 2 '13 at 9:09

2 Answers 2

up vote 1 down vote accepted

$$\int\limits_0^{\pi/2}\int\limits_x^{\pi/2}\frac{\cos y}{y}dydx=\int\limits_0^{\pi/2}\int\limits_0^y\frac{\cos y}{y}dxdy=\left.\int\limits_0^{\pi/2}\cos y\,dy=\sin x\right|_0^{\pi/2}=1$$

share|improve this answer

Hint: define $f(x):=\int_x^{\frac\pi 2}\frac{\cos y}ydy$, and integrate by parts: $$\int_0^{\frac\pi 2}f(x)dx=\frac{\pi}2f\left(\frac{\pi}2\right)-\int_0^{\frac{\pi}2}xf'(x)dx.$$

share|improve this answer

Your Answer

 
discard

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

Not the answer you're looking for? Browse other questions tagged or ask your own question.