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MHT CET20244 May 2024Morning ShiftMathematicsIndefinite IntegrationActual

The integral ^ 2 3 x cosec ^ 4 3 x ~d x is equal to

Options

  1. A3( x)^ - 1 3 + c , (where c is the constant of integration)
  2. B- 3 4 ( x)^ 4 3 + c ,( where c is the constant of integration)
  3. C-3( x)^ - 1 3 + c , (where c is the constant of integration)
  4. D-3( x)^ - 1 3 + c ,( where c is the constant of integration)

Correct answer

D. -3( x)^ - 1 3 + c ,( where c is the constant of integration)

Step-by-step solution

aligned & Let I= ^ 2 3 x cosec ^ 4 3 x & = 1 ^ 2 3 x ^ 4 3 x ~d x & = 1 ( ^ 4 3 x ^ 4 3 x ) ^2 x ~d x & = ^2 x ( x)^ 4 3 ~d x aligned Put x= t ^2 x ~d x= dt I= d t t^ 4 3 d t=-3 t^ 1 3 +c=-3( x)^ -1 3 +c

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