Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET20225 Jul 2022Morning ShiftMathematicsIndefinite IntegrationActual

If I_n= ( ^n x+ ^n x ) d x and I_n- n-1 n I_ n-2 = x x n f(x) , then f(x)=

Options

  1. A^ n-2 x+ ^ n-2 x
  2. B^ n-2 x- ^ n-2 x
  3. C^ n-2 x- ^ n-2 x n
  4. D^ n-2 x+ ^ n-2 x n

Correct answer

B. ^ n-2 x- ^ n-2 x

Step-by-step solution

Here, I_n= ( ^n x+ ^n x ) d xI_n= ^ n-1 x x d x+ ^ n-1 x x d x Using by parts, aligned I_n & .= ^ n-1 x x d x- ( d d x ( ^ n-1 x ) x d x ) ) d x & + ^ n-1 x x d x- ( d d x ( ^ n-1 ) ( d x ) d x . aligned aligned I_n & = ^ n-1 x+ (n-1) ^ n-2 x ^2 x d x & - ^ n-1 x x+ (n-1) ^ n-2 x ^2 x d x aligned array rl I_n= ^ n-1 x x- ^ n-1 & x x + & (n-1) I_ n-2 -(n-1) I_n array aligned I_n(1+n-1)-( & (n-1) I_ n-2 & = ^ n-1 x x- ^ n-1 x x aligned aligned & n (l_n )-(n-1) I_ n-2 = ^ n-1 x x- ^ n-1 x x & I_n- ( n-1 n ) I_ n-2 = x

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