Volume of a solid !?

Question

Find the volume of the solid obtained by rotating the region bounded by y= (1/x^3), y=0, x=1, and x=5, about the y-axis! Please Help! I cannot get the answer and I need it bad

Answer 1

Use the cylindrical shell method. Integrate from x = 1 to x = 5.

∫2πxy dx = 2π∫x(1/x³)dx = 2π∫(1/x²)dx

= -2π/x | [Evaluated from x = 1 to x = 5]

= -2π[1/5 - 1/1] = -2π(-4/5) = 8π/5

Answer 2

graph it out. That will help. Then, Integrate from bounds x= 1 to 5. Use the shells method.