Chapter 4 - Integrals - 4.3 The Fundamental Theorem of Calculus - 4.3 Exercises - Page 327: 7

$g'(x) = \sqrt {x+x^3}$

We are told to find the derivative using Part 1 of the Fundamental Theorem of Calculus given the expression: $g(x) = \int ^{x}_{0}\sqrt {t+t^3}dt$ Since $g(x) = \int^{b}_{a}f(t)dt$ $g'(x) = f(x)$ Thus, $g'(x) = \sqrt {x+x^3}$