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MHT CET202311 May 2023Evening ShiftMathematicsIndefinite IntegrationActual

The value of (1- x) cosec ^2 x ~d x is

Options

  1. A1 2 x 2 + c , where c is a constant of integration.
  2. Bx 2 + c , where c is a constant of integration.
  3. C2 x 2 + c , where c is a constant of integration.
  4. Dx 2 + c , where c is a constant of integration.

Correct answer

B. x 2 + c , where c is a constant of integration.

Step-by-step solution

Let I = (1- x) cosec ^2 ~d x= 2 ^2 x 2 [ x]^2 ~d x [ 1- =2 ^2 2 ] aligned &= 2 ^2 x 2 [2 x 2 x 2 ]^2 ~d x & [ =2 2 2 ] aligned aligned & = 1 2 ^2 x 2 ~d x & = x 2 + c aligned

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