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integrate [sin(x-a)/sin(x+a)] 1/2 w.r.t x

integrate [sin(x-a)/sin(x+a)]1/2 w.r.t x

Grade:12th Pass

1 Answers

Ashwin Muralidharan IIT Madras
290 Points
10 years ago

Hi Suchita,

 

This becomes, (sinxcosa - cosxsina / sinxcosa + cosxsina)1/2

ie (tanx - tana / tanx + tana)1/2

make the substitution tana + tanx = t2

So that the integral becomes 2(-2tana + t2)1/2/{1+{t2-tana)2}

Take t2 common form both the Nr and Dr, and make the substitution tana/t2 = y, so that 1/t3 dt = dy/(-2tana)

In the denominator you will have terms like, {y2/tan2a + (1-y)2}, which is a quadratic.

 

You will get a standard integral of the form ∫(√linear / Quadratic)

Which is integrated by the standard procedure.

 

Hope that helps.

 

All the best,

Regards,

Ashwin (IIT Madras).

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