I'm supposed to find the volume of a graph. The equation of the graph is y=5-2cos(2x). The domain is from 0 to 3 /4. I have tried a million different ways, using integrals to figure this out, unfortunately, every single answer I get is wrong. I've tried u substitution as well as a few other methods, but I do not get a consistent area. I also don't understand how to get the volume from there, especially since if you rotate it, the radius wouldn't be constant.
Answer choices are:
e)8pi + 21pi^2
Help pretty please.
The correct answer is a). When the graph is rotated around the x axis it generates a volume. If you slice this volume with a blade perpendicular to the x axis and make a very thin slice, the slice is a disk whose radius is y or (5-2cos(2x)) the volume of the disk is y^2*pi *dx, where dx is the thickness of the disk. Now integrate this differential volume from 0 to 3pi/4, which gives you the whole volume. The result is: 10pi+20.25pi^2.