Question

f(x) = integrate t ^ 2 dt from 0 to x ^ 3 * ther; f^ prime (x)= Box

Answer 1

Given:

$f(x)=\int_0^{x^2}t^2dt$

Required:

The value of

$f^{\prime}(x)$

Explanation:

Let us solve the integral.

$\begin{gathered} f(x)=\int_0^{x^3}t^2dt \\ \Rightarrow[\frac{t^3}{3}] \\ =\frac{x^9}{9}+c \end{gathered}$

Thus,

$f^{\prime}(x)=x^8$

Final Answer:

The derivative is,

$f^{\prime}(x)=x^8$