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Integrate the functions in Exercises 1 to 24.

    Q7.    \frac{\sin x}{\sin (x-a)}

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We have,         

                                         I\ =\ \frac{\sin x}{\sin (x-a)}   

Assume :-                        (x-a)\ =\ t \Rightarrow \ dx=dt

Putting this in above integral :

                                         \int \frac{\sin x}{\sin (x-a)}dx\ =\ \int \frac{\sin (t+a)}{\sin t}dt

or                                                                           =\ \int \frac{\sin t \cos a\ +\ \cos t \sin a }{\sin t}dt

or                                                                           =\ \int (\cos a\ +\ \cot t \sin a)dt

or                                                                           =\ t\cos a\ +\ \sin a \log |\sin t|\ +\ C

or                                                                            =\ \sin a \log \left | \sin(x-a) \right | + x\cos a\ +\ C

Posted by

Devendra Khairwa

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