What is the volume of the solid produced by revolving f(x)=1/x, x in [1,4] around the x-axis?

1 Answer
Apr 1, 2018

(3pi)/4 units""^3

Explanation:

Volume of revolution about the x axis is given by, V=piinty^2dx, where y is a function of x

In this case y=f[x]=1/x, so V=piint[1/x]^2dx.

1/x^2 can be written as x^-2, this can be integrated using the general power rule, intx^ndx=x^[n+1]/[n+1 , giving int1/x^2dx=-1/x

Therefore the volume will =[-pi/4]-[-pi/1]=(3pi)/4 units""^3