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MHT CET202120 Sep 2021Evening ShiftMathematicsIndefinite IntegrationActual

cosec (x-a) cosec x d x=

Options

  1. Acosec a [ (x-a) cosec x]+c
  2. Bcosec a [ (x-a) x]+c
  3. Ca [ ( x - a ) x ]+ c
  4. Dcosec a [ cosec ( x - a ) x ]+ c

Correct answer

A. cosec a [ (x-a) cosec x]+c

Step-by-step solution

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

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