Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the line y = 6.

Question

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the line y = 6.

y = x

y = 4

x = 0

Answer 1

Integration limits x = 0 and x = 4.

By shell method volume V = 2π∫₀⁴x(6 - x - (6 - 4))dx = 2π∫₀⁴(4x - x²)dx = 2π(2x² - x³/3)₀⁴= 2π(32 - 64/3) =

64π/3