JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Hard

1 of 1

Analyzing +4 | -1

Let

f

be a differentiable function from

R

R

such that

\left| {f(x) - f(y)} \right| \le 2{\left| {x - y} \right|^{\frac{3}{2}}},

for all

x,y \in R.

If f

(0) = 1

, then

\mathrm{ }\int\limits_0^1 {{f^2}(x)dx}

is equal to

View answer and explanation

Correct option: C

Option C (1) is correct because the given condition implies that f'(x) = 0, making f(x) a constant function. Since f(0) = 1, f(x) = 1 for all x, and the integral of f²(x) from 0 to 1 is 1.

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