Integration of siny dx /v(cos³x)(cos(x-y)) . Lower limit is 0, upper limit p/4

Question

siny dx

√(cos³xcos(x-y))

Answer 1

Rahul,

 

∫₀^π/4 (sin y)/√(cos³x cos(x-y)) dx.

 

I am assuming that you just wanted to do one integration, even though there are two variables.

 

Since you are integrating only with respect to (w.r.t) x, anything containing a y should be regarded as a constant.

 

This means you are faced with a VERY difficult integral. While I cannot show you how to do this easily, I need to ask a few questions:

 

1) Is the problem you are posting completely correct?

2) Do you need to do only one integration w.r.t x, or is there a second integration w.r.t y?

3) If there IS a second integration w.r.t y, what are the lower and upper limits?

 

Once you send answers to these, I MIGHT be able to help you better, but I cannot guarantee that the answer will be simple or even possible. There are some integrals (as you may know) that just cannot be done by anybody.

 

Let me know by tomorrow and I will see what I can do for you.