jee-main 2020 Q66

jee-main · India · session1_09jan_shift1 Indefinite & Definite Integrals Definite Integral Evaluation (Computational)
If for all real triplets $( a , b , c ) , f ( x ) = a + b x + c x ^ { 2 }$; then $\int _ { 0 } ^ { 1 } f ( x ) d x$ is equal to:
(1) $2 \left\{ 3 f ( 1 ) + 2 f \left( \frac { 1 } { 2 } \right) \right\}$
(2) $\frac { 1 } { 2 } \left\{ f ( 1 ) + 3 f \left( \frac { 1 } { 2 } \right) \right\}$
(3) $\frac { 1 } { 3 } \left\{ f ( 0 ) + f \left( \frac { 1 } { 2 } \right) \right\}$
(4) $\frac { 1 } { 6 } \left\{ f ( 0 ) + f ( 1 ) + 4 f \left( \frac { 1 } { 2 } \right) \right\}$
If for all real triplets $( a , b , c ) , f ( x ) = a + b x + c x ^ { 2 }$; then $\int _ { 0 } ^ { 1 } f ( x ) d x$ is equal to:\\
(1) $2 \left\{ 3 f ( 1 ) + 2 f \left( \frac { 1 } { 2 } \right) \right\}$\\
(2) $\frac { 1 } { 2 } \left\{ f ( 1 ) + 3 f \left( \frac { 1 } { 2 } \right) \right\}$\\
(3) $\frac { 1 } { 3 } \left\{ f ( 0 ) + f \left( \frac { 1 } { 2 } \right) \right\}$\\
(4) $\frac { 1 } { 6 } \left\{ f ( 0 ) + f ( 1 ) + 4 f \left( \frac { 1 } { 2 } \right) \right\}$