Chapter 5 - The Integral - 5.5 The Fundamental Theorem of Calculus, Part II - Exercises - Page 263: 32

$4x^{5}-2x|x|$

$F(x)$ = $\int_{x^{2}}^{x^{4}}\sqrt{t} dt$ = $\int_{0}^{x^{4}}\sqrt {t}dt$ - $\int_{0}^{x^{2}}\sqrt {t}dt$ apply chain rule with FTC we get $F'(x)$ = $(\sqrt {x^{4}})(4x^{3})-(\sqrt {x^{2}})(2x)$ = $4x^{5}-2x|x|$