jee-main 2023 Q81

jee-main · India · session1_29jan_shift1 Indefinite & Definite Integrals Piecewise/Periodic Function Integration

Let $[ \mathrm { x } ]$ denote the greatest integer $\leq \mathrm { x }$. Consider the function $\mathrm { f } ( \mathrm { x } ) = \max \left\{ \mathrm { x } ^ { 2 } , 1 + [ x ] \right\}$. Then the value of the integral $\int _ { 0 } ^ { 2 } f ( x ) d x$ is :
(1) $\frac { 5 + 4 \sqrt { 2 } } { 3 }$
(2) $\frac { 8 + 4 \sqrt { 2 } } { 3 }$
(3) $\frac { 1 + 5 \sqrt { 2 } } { 3 }$
(4) $\frac { 4 + 5 \sqrt { 2 } } { 3 }$

Let $[ \mathrm { x } ]$ denote the greatest integer $\leq \mathrm { x }$. Consider the function $\mathrm { f } ( \mathrm { x } ) = \max \left\{ \mathrm { x } ^ { 2 } , 1 + [ x ] \right\}$. Then the value of the integral $\int _ { 0 } ^ { 2 } f ( x ) d x$ is :\\
(1) $\frac { 5 + 4 \sqrt { 2 } } { 3 }$\\
(2) $\frac { 8 + 4 \sqrt { 2 } } { 3 }$\\
(3) $\frac { 1 + 5 \sqrt { 2 } } { 3 }$\\
(4) $\frac { 4 + 5 \sqrt { 2 } } { 3 }$

Paper Questions

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