Let f be a differentiable function from R to R such that | f(x) - f(y) | ≤ 2| x - y |^(3/2), for all x,y R. If f(0) = 1 then ∫₀¹ f² (x)dx is equal to:

Integral Calculus: JEE Main 2019 Mathematics question

JEE Main 2019 · 9 Jan, Evening shift · Q3302

JEE Main 20199 Jan, Evening shiftMathematicsMediumIntegral Calculus369× since 2002

Let f be a differentiable function from R to R such that

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

for all

x,y \in

R. If

f\left( 0 \right) = 1

then

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

is equal to :

JEE Main 2019 Integral Calculus Question with Solution (9 Jan Evening shift, Q3302) | JEE Arc