MHT CET20244 May 2024Morning ShiftMathematicsIndefinite IntegrationActual
The integral ^ 2 3 x cosec ^ 4 3 x ~d x is equal to
Options
- A3( x)^ - 1 3 + c , (where c is the constant of integration)
- B- 3 4 ( x)^ 4 3 + c ,( where c is the constant of integration)
- C-3( x)^ - 1 3 + c , (where c is the constant of integration)
- 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