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evaluate the following integral ∫ sin(x – a) / sin(x – b) dx

evaluate the following integral
∫ sin(x – a) / sin(x – b) dx

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 years ago
Ans:
Hello Student,
Please find answer to your question below

I = \int \frac{sin(x-a)}{sin(x-b)}dx
I = \int \frac{sin(x-b+b-a)}{sin(x-b)}dx
I = \int \frac{sin((x-b)+(b-a))}{sin(x-b)}dx
I = \int \frac{sin(x-b)cos(b-a)+cos(x-b)sin(b-a)}{sin(x-b)}dx
I = \int [cos(b-a) + \frac{cos(x-b)sin(b-a)}{sin(x-b)}]dx
I = \int cos(b-a)dx + \int \frac{cos(x-b)sin(b-a)}{sin(x-b)}dx
I = xcos(b-a) + sin(b-a)\int \frac{cos(x-b)}{sin(x-b)}dx
sin(x-b) = t
cos(x-b)dx = dt
I = xcos(b-a) + sin(b-a)\int \frac{1}{t}dt
I = xcos(b-a) + sin(b-a)log(t)+c
I = xcos(b-a) + sin(b-a)log(sin(x-b))+c

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