Differential Equations Activity #1 Question 1

Question

.1.Find the volume of the solid when rotating about the x-axis.

.y= 1/x, x-axis, x=1 and x=3

Answer 1

If using the disc method, the integral will be the integral of pi*y² over the x range of 1 - 3.

The integral is just pi*Integral (1 - 3) of y² dx which is the same as pi*integral (1 - 3) of 1/x² dx

which equals -pi/x (1 - 3) which equals 2*pi/3 = 2.094.

If you use the Pappus formula, you will need the y area centroid and the area under the curve. The area under the curve is 1.0986 and the y area centroid is .3034. So, the volume of revolution is 2*pi*.3034*1.0986 = 2.094