Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
COMEDK2025MathematicsDefinite IntegrationActual

_ 6 ^ 3 1 1+ x d x=

Options

  1. A3
  2. B2
  3. C6
  4. D12

Correct answer

D. 12

Step-by-step solution

Let I = _ 6 ^ 3 1 1 + x dx . Using the property _ a ^ b f(x) dx = _ a ^ b f(a + b - x) dx , we have a + b = 6 + 3 = 2 . I = _ 6 ^ 3 1 1 + ( 2 - x) dx = _ 6 ^ 3 1 1 + x dx . I = _ 6 ^ 3 1 1 + 1 x dx = _ 6 ^ 3 x x + 1 dx . Adding the two expressions for I : 2I = _ 6 ^ 3 ( 1 1 + x + x 1 + x ) dx = _ 6 ^ 3 1 dx . 2I = [x]_ 6 ^ 3 = 3 - 6 = 6 . I = 12 . Answer: 12

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 COMEDK PYQs