# How do you use the second fundamental theorem of Calculus to find the derivative of given int sqrt((t^3)+1) from [-1, x]?

Aug 10, 2016

$\sqrt{\left({x}^{3}\right) + 1}$

#### Explanation:

FTC part 1 tells us that

$\frac{d}{\mathrm{dx}} \left({\int}_{a}^{x} f \left(t\right) \mathrm{dt}\right) = f \left(x\right)$

so $\frac{d}{\mathrm{dx}} \left({\int}_{- 1}^{x} \sqrt{\left({t}^{3}\right) + 1} \mathrm{dt}\right)$

$\sqrt{\left({x}^{3}\right) + 1}$