Answer
As a result $F_\alpha=-\sqrt{\alpha^3+1}$, $F_\beta=\sqrt{\beta^3+1}$.
Work Step by Step
$F(\alpha,\beta)=\int_\alpha^\beta\sqrt{t^3+1}dt$
In order to find $F_\alpha$ we treat$\beta$ as a constant and differentiate with respect to $\alpha$.
$F_\alpha=-\sqrt{\alpha^3+1}$
In order to find $F_\beta$ we treat $\alpha$ as a constant and differentiate with respect to $\beta$.
$F_\beta=\sqrt{\beta^3+1}$
