Question

Find the volume of the solid obtained by rotating the region under the graph of the function f(x)=2/x+1 about the x-axis over the interval [1,3].

Answer 1

f(x)=2/x+1

y = 2/x + 1

vol = π∫ y^2 dx from 1 to 3
= π∫ (2/x + 1)^2 dx from 1 to 3
= π∫ (4/x^2 + 4/x + 1) dx from 1 to 3
=π [-4/x + 4ln(x) + x]| from 1 to 3
= π( -4/3 + 4ln4 + 3 - (-4 + 4ln1 + 1) ) , remember ln1 = 0
= ......