247. $\int_{0}^{2} 3 x^{4} d x . \quad$ 248. $\int_{-1}^{\sqrt{3}} 4 t^{3} d t . \quad$ 249. $\int_{0}^{1} \sqrt[3]{x} d x$.
Solution. $\int_{0}^{1} \sqrt[3]{x} d x=\int_{0}^{1} x^{1 / 3} d x=\left.\frac{3}{4} x^{4 / 3}\right|_{0} ^{1}=\frac{3}{4}\left(1^{1 / 3}-0^{4 / 3}\right)=\frac{3}{4}$.