Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET201822 Apr 2018Morning ShiftMathematicsIndefinite IntegrationActual

For n 2 , If I_n= ^n x d x , then I₄- 2 3 I₂=

Options

  1. A^2 x x+c
  2. B1 3 ^2 x x+c
  3. C2 3 ^2 x x+c
  4. 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

Practice Indefinite Integration on Quantrex Academy →

More from Indefinite Integration

If 5 x x -2 dx = ax + b | x -2 x |+ c , then a + b = 2025x Cos ⁻¹ ( 1-x^2 1+x^2 ) d x(x>0)= 2025d x (1+ x ) x-x^2 = 2025If x x x+1 ~d x= f (x)+ k , then f ( 4 )= 2025If x^4+1 x^2+1 d x=A x^3+B x^2+C x+D Tan ⁻¹ x+E , then A+B+C+D= 2025If x^2-x+2 x^2+x+2 d x=x- (f(x))+ 2 7 Tan ⁻¹(g(x))+c , then f (-1)+ 7 ~g (-1)= 2025(x- 3 ) (x+ 6 ) d x= 2025If a x+3 x 5 x+2 x d x= 26 29 x- k 29 |5 x+2 x|+c , then |a+k|= 2025 Full Indefinite Integration list All AP EAMCET PYQs