Question

If $f\,\,\left( x ight) = \,\,\left\{ {\begin{array}{*{20}{c}} {1 - x,}\ {0,}\ {{{\left( {2 - x} ight)}^2},} \end{array}\,\,\begin{array}{*{20}{c}} {0 \le \,\,\,x\,\, \le 1}\ {1 \le \,\,\,x\,\, \le 2}\ {2 \le \,\,\,x\,\, \le 3} \end{array}} ight.$ and $\phi \,\,\left( x ight) = \mathop \smallint \limits_0^x \,\,f\,\left( t ight)\,\,dt$. Then, for any $x \in \left[ {2,3} ight],\,\,\phi \,\,\left( x ight)$ equals

Accepted Answer

$\frac{1}{2}\,\, + \,\,\frac{{{{\left( {x - 2} \right)}^3}}}{3}$

Answer

$\frac{{{{\left( {x - 2} \right)}^3}}}{3}$

Answer

$\frac{1}{2}\,\, - \,\,\frac{{{{\left( {x - 2} \right)}^3}}}{3}$

Answer

None of these

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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