Choose the appropriate method (disk or washer) to find the volume of the solid generated by revolving the shaded region about the given axis.

Question

about the x-axis

y = 3sec x

A) 21/2 π

B) 9/2 π

C) 9π

D) 3π

Answer 1

So to think about this intuitively, recall that the volume of a disk is πr²h, where r is the radius and h is the height.

You might recall that the integral of a function is the area under the curve and that the way to think about this is the sum of the areas of a bunch of infinitely small rectangles where the "height" of each rectangle is the output value of the function at each point.

Similarly, you are finding the sum of the volumes of a bunch of infinitely thin disks, and you can think of your "radius" as the output value of y=3sec(x) at each point. This is how the following formula for the volume of the solid generated by rotating the curve about the x-axis is derived:

∫_a^b π (y)^2 dx where y=3sec x in your case, and (a, b) is the interval you are taking the integral across (which I don't see in the question...)

I hope this helps.

EDIT: formatting, spelling