JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Medium

1 of 1

Analyzing +4 | -1

Let

f

be a differentiable function from

\mathbf{R}

\mathbf{R}

such that

[f(x)

-f(y)|\leq 2| x-\left.y\right|^{3 / 2}

, for all

x, y, \in \mathbf{R}

. If

f(0)=1

then

\int\limits_{0}^1 f^2(x) d x

is equal to:

View answer and explanation

Correct option: A

Option A (1) is correct because the given condition implies that

f(x)

is a constant function, and since

f(0) = 1

f(x) = 1

for all

x

More Questions from DEFINITE INTEGRATION

Practice All Chapter MCQs →

\int \nolimits_0^\infty \,\,\log \,\,\left( {x + \frac{1}{x}} \right)\,\,\frac{{dx}}{{1 + {x^2}}}

f\left( x \right)

\int \nolimits_0^{{t^2}} \,\,x\;\,f\left( x \right)\,\,dx = \frac{2}{5}\,\,{t^5}

f\left( {\frac{4}{{25}}} \right)

\int\limits_{{0}}^{11}[x]^{3} . \mathrm{dx}

[*]

\int\limits_{2}^4 \frac{\log x^2}{\log x^2+\log \left(36-12 x+x^2\right)} d x

\int\limits_{{-2}}^0\left(x^3+3 x^2+3 x+3+(x+1) \cos (x+1)\right) d x

I\,\,\left( {m,\,\,n} \right) = \int \nolimits_0^1 \,\,{t^m}\,\,{\left( {1 + t} \right)^n}\,\,dt

I\left( {m,\,\,n} \right)

I\,\,\left( {m + 1,\,\,n + 1} \right)