Let the region R be the area enclosed by the function f(x)=ln(x) and g(x)= 1/2x-2. Find the volume of the solid generated when the region R is revolved about the line y=-5.

Step-by-step explanation:

This problem can be solved by using the expression for the Volume of a solid with the washer method

where R and r are the functions f and g respectively (f for the upper bound of the region and r for the lower bound).

Before we have to compute the limits of the integral. We can do that by taking f=g, that is

there are two point of intersection (that have been calculated with a software program as Wolfram alpha, because there is no way to solve analiticaly)

x1=0.14

x2=8.21

and because the revolution is around y=-5 we have

and by replacing in the integral we have

and by evaluating in the limits we have

Hope this helps

regards

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