about \(\displaystyle x = 4\) so revolves about y axis

Find limit of integration

\(\displaystyle 3x^{4} = 0\)

\(\displaystyle x = 0 \)

\(\displaystyle V = 2\pi \int_{0}^{2} (x)(3x^{4}) dx \)

\(\displaystyle V = 2\pi \int_{0}^{2} 3x^{5}) dx\)

\(\displaystyle V = (2\pi) \dfrac{3x^{6}}{6}\) evaluated at 0 and 2

\(\displaystyle V = (2\pi) \dfrac{x^{6}}{2}\) evaluated at 0 and 2

\(\displaystyle V = (2\pi) [[\dfrac{(2)^{6}}{2}] - [0]] = 32 * 2\pi = 64 \pi\) - wrong on homework ?