Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
Most Important Selected Qs for JEE AdvancedMathematicsDefinite Integration

If I_n= _ -1 ^1|x| (1+x+ x^2 2 + x^3 3 + + x^ 2 n 2 n ) d x , then:

Options

  1. AI₂= 4 3
  2. BI₂= 7 6
  3. C_ n I_n= 3 2
  4. D_ n I_n= 5 4

Correct answer

C. _ n I_n= 3 2

Step-by-step solution

I_n=2 ₀^1 x (1+ x^2 2 + x^4 4 + . .+ x^ 2 n 2 n ) d x ( _ -1 ^1( . odd .) d x=0 ) aligned & =2 ( x^2 2 + x^4 2 4 + x^6 4 6 + . .+ x^ 2 n+2 2 n(2 n+2) )₀^1 & =1+ 1 2 [ (1- 1 2 )+ ( 1 2 - 1 3 )+ + ( 1 n - 1 n+1 ) ] & =1+ 1 2 (1- 1 n+1 ) aligned I₂=1+ 1 2 (1- 1 3 )= 4 3 and I_ = 3 2

Practice Definite Integration on Quantrex Academy →

More from Definite Integration

The value of the definite integral ₀² 1 3^ x+3 2 , dx is 2026The value of the integral ₀² x(x^2+x+1) ( x+1 )( x^4+x^2+1 ) , dx is equal to: 2026If _ /6 ^ /4 ( (x- 3 ) (x+ 3 )+1 )dx = _e( 3 -1) , then 9 ^2 is equal to ________. 2026Let A = bmatrix 1 & 3 & -1 2 & 1 & 0 & 1 & -1 bmatrix be a singular matrix. Let f(x) = ₀^x (t^2 + 2t + 3) ,dt , x [1, ] . If M and m are respectively the maximum and the minimum va 2026Let f: R R be such that f(xy) = f(x)f(y) , for all x, y R and f(0) 0 . Let g: [1, ) R be a differentiable function such that x^2 g(x) = ₁^x (t^2 f(t) - tg(t)) ,dt . Then g(2) is eq 2026The value of the integral _ -1 ¹ ( x^3 + |x| + 1 x^2 + 2|x| + 1 ) dx is equal to : 2026The value of the integral _ - /4 ^ /4 ( 32 ^4 x 1 + e^ x )dx is: 2026Let (2^ 1-a + 2^ 1+a ) , f(a) , (3^a + 3^ -a ) be in A.P. and be the minimum value of f(a) . Then the value of the integral _ _e( -1) ^ _e( ) dx (e^ 2x - e^ -2x ) is : 2026 Full Definite Integration list All Most Important Selected Qs for JEE Advanced PYQs