Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
Manipal MET2023MathematicsLimits

If F: R R is a differentiable function and f(3)=6 , then _ x 3 ₆^ f(x) 2 t d t (x-2) is equal to

Options

  1. A18 f^ (3)
  2. B0
  3. C24 f^ (3)
  4. D3 f^ (3)

Correct answer

A. 18 f^ (3)

Step-by-step solution

Let I= _ x 3 ₆^ f(x) 2 t x-2 d t [ 0 0 . form, as .f(3)=6 ] On applying the L' Hospital rule, we get I= _ x 3 ₆^ f(x) 2 f(x) f^ (x) 1 ( f(3)=6) So, I=3 f(3) f^ (3)=18 f^ (3) _ x 3 ₆^ f(x) 2 t d t x-2 =18 f^ (3)

Practice Limits on Quantrex Academy →

More from Limits

If _ x 0 ( p 2x + 1 - 2x x + x ) = 1 then the value of ' p ' is 2026_ x 2 ( 1 - x x ) is equal to 2026The value of _ x 3 [ 1 x-3 + 9x 27-x^3 ] is: 2026_ x 0 (1 - 2x)(3 + x) x 4x is equal to: 2026If _ x 3 ( x^2 - ax - 3b x - 3 ) = 5 , then a + b = 2026If f(x) = cases x^2 - 1 & if x 2 x + 1 & if x < 2 cases , then _ x 1 f(x) + _ x 2 f(x) = 2026_ x 4 2 2 -( x+ x)^3 1- 2 x = 2025Let [x] denote the greatest integer less than or equal to x . Then _ x 2⁺ ( [x]^3 3 - [ x 3 ]^3 )= 2025 Full Limits list All Manipal MET PYQs