Latex test

I haven't done latex in a while so $\int_0^{k} 2\sqrt[2]{x} dx \ for \ 2*\int_0^{k} \sqrt[2]{x}dx \ = \ 2[\frac{2(x^3/2)}{3} |^{k}_0] = \frac{32}{3}, \ 2*\frac{2(\sqrt[2]{k^3})}{3} \ = \ \frac{32}{3}. \ k \ = \ 4 \ for \ all \ real \ solutions.$