AP EAMCET201822 Apr 2018Morning ShiftMathematicsIndefinite IntegrationActual
For n 2 , If I_n= ^n x d x , then I₄- 2 3 I₂=
Options
- A^2 x x+c
- B1 3 ^2 x x+c
- C2 3 ^2 x x+c
- D1 2 | x+ x|+c
Correct answer
B. 1 3 ^2 x x+c
Step-by-step solution
We have, aligned & I_n= ^n x d x & I₂= ^2 x d x= x+c₁ & and I₄= ^4 x d x & = ^2 x ^2 x d x & = ( ^2 x+1 ) ^2 x d x & = ^3 x 3 + x+c₂ & = 1 3 ^3 x+ 1 3 x+c & I₄ 3 I₂= ^3 x 3 + x+c₂- 2 3 x- 2 c₁ 3 & = 1 3 x ( ^2 x+1 )+c & = 1 3 x ^2 x+c aligned