다음 적분을 구하라.
$$\int_0^8\sqrt[3]{x}dx$$
풀이
\(\displaystyle\int_0^8\sqrt[3]{x}dx=\int_0^8x^{\frac{1}{3}}dx=\left[\frac{3}{4}x^{\frac{4}{3}}\right]_0^8=\left[\frac{3}{4}x\sqrt[3]{x}\right]_0^8\)
\(\displaystyle=\frac{3}{4}(8)\sqrt[3]{8}-\frac{3}{4}(0)\sqrt[3]{0}=6\sqrt[3]{2^3}-0=6(2)=12\)