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)`

Step-by-step explanation:

Let us solve the integral.

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

Thus,

`f^(\prime)(x)=x^8`

Final Answer:

The derivative is,

`f^(\prime)(x)=x^8`