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MHT CET202415 May 2024Evening ShiftMathematicsIndefinite IntegrationActual

cosec (x-a) cosec x d x=

Options

  1. A-1 a ( (x- a ) x)+ c , where c is a constant of integration.
  2. B1 a ( (x- a ) x)+ c , where c is a constant of integration.
  3. C1 a ( (x- a ) cosec x)+ c , where c is a constant of integration.
  4. D-1 a ( cosec (x- a ) x)+ c , where c is a constant of integration.

Correct answer

C. 1 a ( (x- a ) cosec x)+ c , where c is a constant of integration.

Step-by-step solution

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

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