Question

If ${\int }_{ln2}^{x^2(1+x)}f\left(t\right)dt=x,$ then value of $f\left(2\right)$ is

• A. $\frac{1}{2}$
• B. $\frac{1}{3}$
• C. $\frac{1}{4}$
• D. $\frac{1}{5}$

Answer 1

The correct option is D

$\frac{1}{5}$

Differentiating both sides w.r.t. x, then

$f\left(x^2\right(1+x\left)\right)\times (2x+3x^2)=1$

At $x=1\Rightarrow f\left(2\right)=\frac{1}{5}$