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MHT CET20244 May 2024Morning ShiftMathematicsIndefinite IntegrationActual

If I= e^ ( + cosec ^2 ) d , then I is equal to

Options

  1. Ae ^ ( + cosec ^2 )+ c , (where c is a constant of integration)
  2. Be ^ ( + cosec )+ c , (where c is a constant of integration)
  3. Ce ^ ( - cosec )+ c , (where c is a constant of integration)
  4. De ^ ( - cosec ^2 )+ c , ( where c is a constant of integration)

Correct answer

C. e ^ ( - cosec )+ c , (where c is a constant of integration)

Step-by-step solution

aligned & Let =t & d =d t & = e^t ( t+ 1 t^2 ) d t & = e^t t d t+ e^t t^2 d t & = t e^t- e^t t d t+ [ e^t -t - e^t -t d t ]+c & = t e^t- e^t t d t- e^t t + e^t t d t+c & =e^t [ t- 1 t ]+c & =e^ [ - cosec ]+c aligned

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