Finding Surface Area of Rotating a Curve?

Question

I am having trouble figuring out how to find the surface area of the following curve rotated around the Y axis from y=0 to y=3................ x= 3 e^(2y)

Answer 1

I'm assuming you are familiar with calculus. Consider an infinitesimal cylinder at height 'y' of thickness 'dy'. The surface area of that cylinder is 2*pi*Radius*thickness. Here the radius is simply 3e^2y, and 'dA' the infinitesimal area is given by 2*pi*3e^2y*dy. To get the total area gotten by rotating this curve, (note we don't have to do any rotation as its already factored in by the assuming an infinitesimal cylinder) simply integrate between 0-3 the above expression, which I leave as an excercise for you. Hope this helps.