integral problem for the ratio of sine functions

upingman

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Aug 10, 2018
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Hi everyone,

I'm currently stuck in an integral problem as follows (also attached):

Solve the integral of sin(x-y)/sin(x-a) w.r.t. x and y, where x is from 0 to y, and y from 0 to b. a and b are given constants.

I tried to put the integral to the nominator and denominator respectively to get the approximation, while the numerical evaluation shows this approximation isn't reasonable tight. So, I would greatly appreciate if anyone could give me some suggestion or hint on the calculation of this integral problem. If it isn't possible to get the exact solution, the reasonable approximation is also very welcome.

Many thanks,
Upingman
 

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Hi everyone,

I'm currently stuck in an integral problem as follows (also attached):

Solve the integral of sin(x-y)/sin(x-a) w.r.t. x and y, where x is from 0 to y, and y from 0 to b. a and b are given constants.

I tried to put the integral to the nominator and denominator respectively to get the approximation, while the numerical evaluation shows this approximation isn't reasonable tight. So, I would greatly appreciate if anyone could give me some suggestion or hint on the calculation of this integral problem. If it isn't possible to get the exact solution, the reasonable approximation is also very welcome.

Many thanks,
Upingman
Hint:

Use sin(x-y) = sin(x)*cos(y) - cos(x)*sin(y)
 
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