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

glide reflection.

its mainly because the pattern will be infinite and will never end. it will look like a gilder or like a filpbook when set to motion.

step-by-step explanation: