Question

Find the volume of the solid revolution generated by rotating the curve y = x² bounded by x = 3 and y = 0; about the y-axis

Answer 1

$V = \int_{0}^{3} 2\pi x\times(x^2 ) dx =$

$= 2\pi \int_{0}^{3} x^3 dx = 2\pi [\frac{x^4}{4} ] \Big\vert_{0}^{3}$

$= 2\pi [\frac{81}{4}-0] = 2\pi [\frac{81}{4}] = \frac{81 \pi}{2}$

Answer

$V = \frac{81\pi}{2}$