Question

F(x) = integrate t ^ 4 dt from 0 to x ^ 2 * then

Answer 1

The given function is:

`f(x)=\int_0^(x^2)t^4dt`

Therefore, by evaluating the integral on the right hand side, it follows that:

`\begin{gathered} f(x)=(t^(4+1))/(4+1)\biggr\rvert_0^(x^2) \\ f(x)=(t^5)/(5)\biggr\rvert_0^(x^2) \\ f(x)=((x^2)^5)/(5)-((0)^5)/(5) \\ f(x)=(x^(10))/(5) \end{gathered}`

Therefore, by differentiating with respect to x, it follows that:

`\begin{gathered} f^(\prime)(x)=10*(x^(10-1))/(5) \\ f^(\prime)(x)=2x^9 \end{gathered}`

Therefore,

f'(x) = 2x⁹