Question

If $f\left(x\right)+2f(1-x)=x^2+1\forall x\in R$ and ${\int }_0^{k}f\left(X\right)dx=0$, then k equals to

• A. 3
• B. 2
• C. 4
• D. none of these

Answer 1

The correct option is A 3

Putting (1 – x) for x and subtracting we get $f\left(x\right)=\frac{x^2-4x+3}{3}$
Now ${\int }_0^k\frac{x^2-4x+3}{3}dx=0\Rightarrow \frac{k^3}{3}-2k^2+3k=0$
$\Rightarrow k=3$