Question

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y=1/x^3,y=0,x=4,x=7. About the y-axis.
Volume =

Answer 1

v = ∫[4,7] 2πrh dx
where r=x and h=y=1/x^3

or,

v = ∫[1/343,1/64] π(R^2-r^2) dy
where r=4 and R=1/&$x221B;y

Answer 2

that's R=1/cbrt(y)

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