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MHT CET202313 May 2023Evening ShiftMathematicsDefinite IntegrationActual

The integral _ 6 ^ 3 ^ 2 3 x cosec ^ 4 3 x ~d x is equal to

Options

  1. A3^ 5 6 -3^ 2 3
  2. B3^ 7 6 -3^ 5 6
  3. C3^ 5 3 -3^ 1 3
  4. D3^ 4 3 -3^ 1 3

Correct answer

B. 3^ 7 6 -3^ 5 6

Step-by-step solution

Let I = _ 6 ^ 3 ^ 2 3 x cosec ^ 4 3 x ~d x= _ 6 ^ 3 d x ^ 2 3 x ^ 4 3 x = _ 6 ^ 3 ^2 x ^ 4 3 x ~d x Put x= t ^2 x ~d x= dt I= _ 1 3 ^ t^ 3 3 dt 4 3 = [-3 t ^ - 1 3 ]_ 1 3 ^ 3 =-3 [( 3 )^ -1 3 - ( 1 3 )^ -1 3 ]=-3 (3^ - 1 6 -3^ 1 6 )=3^ 7 6 -3^ 5 6

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