Question

f(x)= int 0 ^ x (t^ 3 +7t^ 2 +4) dt then

Answer 1

Since the given function is

$f(x)=\int_0^x(t^3+7t^2+4)dt$

That means

$f^{\prime}(x)=(t^3+7t^2+4)$

Then to find f''(x) we will differentiate f'(x) with respect to t

$\begin{gathered} f“(x)=3t^{3-1}+7(2)t^{2-1}+0 \\ \\ f“(x)=3t^2+14t \end{gathered}$

The answer is

$f“(x)=3t^2+14t$