jee-main 2021 Q75

jee-main · India · session2_17mar_shift2 Indefinite & Definite Integrals Piecewise/Periodic Function Integration

If the integral $\int _ { 0 } ^ { 10 } \frac { [ \sin 2 \pi x ] } { \mathrm { e } ^ { x - [ x ] } } d x = \alpha e ^ { - 1 } + \beta e ^ { - \frac { 1 } { 2 } } + \gamma$, where $\alpha , \beta , \gamma$ are integers and $[ x ]$ denotes the greatest integer less than or equal to $x$, then the value of $\alpha + \beta + \gamma$ is equal to:
(1) 0
(2) 20
(3) 25
(4) 10

If the integral $\int _ { 0 } ^ { 10 } \frac { [ \sin 2 \pi x ] } { \mathrm { e } ^ { x - [ x ] } } d x = \alpha e ^ { - 1 } + \beta e ^ { - \frac { 1 } { 2 } } + \gamma$, where $\alpha , \beta , \gamma$ are integers and $[ x ]$ denotes the greatest integer less than or equal to $x$, then the value of $\alpha + \beta + \gamma$ is equal to:\\
(1) 0\\
(2) 20\\
(3) 25\\
(4) 10

Paper Questions

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