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KCET2009MathematicsIndefinite Integration

cosec (x-a) cosec x d x is equal to

Options

  1. A-1 a | x cosec (x-a)|+c
  2. B-1 a [ (x-a) x]+c
  3. C1 a [ (x-a) cosec x]+c
  4. D1 a [ (x-a) x]+c

Correct answer

A. -1 a | x cosec (x-a)|+c

Step-by-step solution

Let I= cosec (x-a) cosec x d x= a a (x-a) x d x=- 1 a [(x-a)-x] (x-a) x d x=- 1 a [ (x-a) x- (x-a) x (x-a) x ] d x=- 1 a [ x- (x-a)] d x=- 1 a [ | x|- | (x-a)|]+c= -1 a [ | x cosec (x-a)|]+c

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