Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
Black Book Advanced Problems in MathematicsMathematicsIndefinite and Definite Integration

Let f:(0, 1) (0, 1) be a differentiable function such that f'(x) 0 for all x (0, 1) and f ( 1 2 ) = 3 2 . Suppose for all x , _ t x ₀^t 1 - (f(s))^2 ds - ₀^x 1 - (f(s))^2 ds f(t) - f(x) = f(x) . Then the value of f ( 1 4 ) belongs to :

Options

  1. A7 4 , 15 4
  2. B7 3 , 15 3
  3. C7 2 , 15 2
  4. D7 , 15

Correct answer

A. 7 4 , 15 4

Step-by-step solution

Open this question in the Quantrex Academy app for the full interactive solution, figures and similar PYQs.

Practice Indefinite and Definite Integration on Quantrex Academy →

More from Indefinite and Definite Integration

**Paragraph for Question Nos. 1 to 2** Let f(x) = x^2 ^2 x (2x + 6 x - 2x ^2 x) dx and f(x) passes through the point ( , 0) If f : R - (2n + 1) 2 R then f(x) be a :**Paragraph for Question Nos. 1 to 2** Let f(x) = x^2 ^2 x (2x + 6 x - 2x ^2 x) dx and f(x) passes through the point ( , 0) The number of solution(s) of the equation f(x) = x^3 in **Paragraph for Question Nos. 3 to 4** Let f(x) be a twice differentiable function defined on (- , ) such that f(x) = f(2 - x) and f' ( 1 2 ) = f' ( 1 4 ) = 0 . Then The minimum nu**Paragraph for Question Nos. 3 to 4** Let f(x) be a twice differentiable function defined on (- , ) such that f(x) = f(2 - x) and f' ( 1 2 ) = f' ( 1 4 ) = 0 . Then _ -1 ^1 f'(1 +**Paragraph for Question Nos. 3 to 4** Let f(x) be a twice differentiable function defined on (- , ) such that f(x) = f(2 - x) and f' ( 1 2 ) = f' ( 1 4 ) = 0 . Then ₀^2 f(1 - t) e**Paragraph for Question Nos. 6 to 8** Consider the function f(x) and g(x) , both defined from R Rf(x) = x^3 2 + 1 - x ₀^x g(t) dt and g(x) = x - ₀^1 f(t) dt , then Minimum value o**Paragraph for Question Nos. 6 to 8** Consider the function f(x) and g(x) , both defined from R Rf(x) = x^3 2 + 1 - x ₀^x g(t) dt and g(x) = x - ₀^1 f(t) dt , then The number of p**Paragraph for Question Nos. 6 to 8** Consider the function f(x) and g(x) , both defined from R Rf(x) = x^3 2 + 1 - x ₀^x g(t) dt and g(x) = x - ₀^1 f(t) dt , then The area bounde Full Indefinite and Definite Integration list All Black Book Advanced Problems in Mathematics PYQs