Find volume of the solid obtained by rotating the region enclosed by 𝑦=1/𝑥^4, 𝑦=0, 𝑥=3, 𝑥=6 about the line 𝑥=−1. Compute using the method of cylindrical shells via an integral

Answer 1

By Shell Method V = 2π∫₃⁶(x + 1)(1/x⁴)dx = 2π∫₃⁶(x^-3 + x^-4)dx = 2π(- x^-2/2 - x^-3/3)₃⁶ = - π(1/x² + (2/3)/x³)₃⁶ =

0.33