If for all real triplets a , b , c , f x = a + b x + c x 2 ; then ∫ 0 1 f x d x is equal to:

1. $2\left\{3f\left(1\right)+2f\left(\frac{1}{2}\right)\right\}$
2. $\frac{1}{2}\left\{f\left(1\right)+3f\left(\frac{1}{2}\right)\right\}$
3. $\frac{1}{3}\left\{f\left(0\right)+f\left(\frac{1}{2}\right)\right\}$
4. $\frac{1}{6}\left\{f\left(0\right)+f\left(1\right)+4f\left(\frac{1}{2}\right)\right\}$

Solution

Asked in: JEE Main 2020 (09 Jan Shift 1)

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