JEE Main 2020 (9 Jan, Shift 1) Maths Q51: Integrals

Question

If for all real triplets (a, b, c), $f(x)=a+bx+cx^2$; then $\int_0^1 f(x)\,\mathrm{d}x$ is equal to :

Accepted Answer

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

Answer

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

Answer

$\frac{1}{2}\left\{f(1)+3f\left(\frac{1}{2}\right)\right\}$

Answer

$2\left\{3f(1)+2f\left(\frac{1}{2}\right)\right\}$

Answer

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

JEE Main 9 January 2020, Shift 1, Maths Q51