The difference between the greatest and least values of the function $\phi \,\,\left( x \right) = \mathop \smallint \limits_0^x \left( {t + 1} \right)\,\,dt$ on $\left[ {{\rm{2, 3}}} \right]$, is

${\rm{11}}\,{\rm{/}}\,{\rm{2}}$

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

The difference between the greatest and least values of the function

\phi \,\,\left( x \right) = \int \limits_0^x \left( {t + 1} \right)\,\,dt

\left[ {\mathrm{2, 3}} \right]

, is

View answer and explanation

Correct option: C

\mathrm{7}\,\mathrm{/}\,\mathrm{2}

Option C is correct because the difference between the greatest and least values is found by evaluating the definite integral at the bounds and subtracting.

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}}}

is equal to If

f\left( x \right)

is differentiable and

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

, then

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

equals The value of

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

, where

[*]

denotes the greatest integer function, is The integral

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

is equal to: The definite integral

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

equals If

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

,then the expression for

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

in terms of

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