Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
KVPY2011MathematicsDefinite Integration

Let [x] denote the largest integer not exceeding x and x =x-[x] . Then ₀²⁰¹² e^ ( x ) e^ ( x ) +e^ - ( x ) d x is equal to -

Options

  1. A0
  2. B1006
  3. C2012
  4. D2012

Correct answer

B. 1006

Step-by-step solution

I =2012 ₀¹ e^ x e^ x +e^ - x d x using king property I =2012 ₀¹ e^ - x e^ - x +e^ x d x 2 I =2012 I =1006

Practice Definite Integration on Quantrex Academy →

More from Definite Integration

₀^1 2 x+5 x^2+3 x+2 ~d x= 2025₀^1 x^ 5 / 2 (1-x)^ 3 / 2 ~d x= 2025_ n [ 1 n^2 ^2 1 n^2 + 2 n^2 ^2 4 n^2 + 3 n^2 ^2 9 n^2 + + 1 n^2 ^2 1 ]= 2025₀^1 x Sin ⁻¹ x d x= 2025_ - 2 ^ 2 (x-[x]) d x= 2025₀^2 x^2(2-x)^5 d x= 2025If f(x)= Max x^3-4, x^4-4 , and g(x)= Min x^2, x^3 , then _ -1 ^1(f(x)-g(x)) d x= 2025_ n 2 n [ 2 n + 2 2 n + 3 2 n + + 2 ]= 2025 Full Definite Integration list All KVPY PYQs