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AP EAMCET202022 Sep 2020Evening ShiftMathematicsIndefinite IntegrationActual

e^ x cosec x cosec x (1-x x) d x=

Options

  1. Ae^ x x +c
  2. Be^ x cosec x +c
  3. Ce^ -x cosec x +c
  4. De^ -x x +c

Correct answer

B. e^ x cosec x +c

Step-by-step solution

e^ x cosec x cosec x(1-x x) d x Put, x cosec x=t Differentiate w.r.to ' x ' aligned & x d d x cosec x+ cosec x d d x x= d d x t & x(- cosec x x)+ cosec x(1)= d t d x & cosec x(1-x x) d x=d t= e^t d t &=e^t+c=e^ x cosec x +c aligned Hence, option (2) is correct.

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