Question

If f(x) is a differentiable function and ${\int }_0^{x^3}{t}^{2}f\left(t\right)dt=\frac{3}{13}{x}^{13}+5$ then $f\left(\frac{8}{27}\right)$

• A. $\frac{8}{27}$
• B. $\frac{16}{27}$
• C. $\frac{16}{81}$
• D. $\frac{8}{9}$

Answer 1

The correct option is C $\frac{16}{81}$

Diff. w.r.t. $x\Rightarrow f\left(x^3\right)=x^4$