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AP EAMCET2010MathematicsIndefinite Integration

If (1- x) cosec ^2 x d x=f(x)+c , then f(x) is equal to

Options

  1. Ax 2
  2. Bx 2
  3. C2 x 2
  4. D1 2 x 2

Correct answer

A. x 2

Step-by-step solution

(1- x) cosec ^2 x d x= (2 ^2 x 2 ) 1 ^2 x d x [ x=1-2 ^2 x 2 ]=2 ^2 x 2 (2 x 2 x 2 )^2 d x [ x=2 x 2 x 2 ]=2 x 2 x 2 2 2 ^2 x 2 ^2 x 2 d x= 1 2 ^2 x 2 d x= 1 2 x 2 2+c= x 2 +c=f(x)+c f(x)= x 2

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