MHT CET202311 May 2023Morning ShiftMathematicsIndefinite IntegrationActual
Let f (x)= x (1+x)^2 ~d x, x 0 , then f (3)- f (1) is equal to
Options
- A- 6 + 1 2 + 3 4
- B- 12 + 1 2 + 3 4
- C6 + 1 2 - 3 4
- D6 + 1 2 - 3 4
Correct answer
D. 6 + 1 2 - 3 4
Step-by-step solution
aligned & f (x)= x (1+x)^2 ~d x, x 0 & f (3)- f (1)= ₁^3 x (1+x)^2 ~d x= I ( say ) aligned Put x = d x=2 ^2 d When x=1, = 4 and when x=3, = 3 aligned I & = _ 4 ^ 3 2 ^2 ^2 (1+ ^2 )^2 d & = _ 4 ^ 3 2 ^2 1+ ^2 d & = _ 4 ^ 3 2 ^2 + ^2 d & = _ 4 ^ 3 (1- 2 ) d & = [ - 2 2 ]_ 4 ^ 3 & = ( 3 - 4 )- 1 2 ( 3 2 -1 ) & = 12 - 3 4 + 1 2 aligned