Find the Surface Area

Question

Find the Surface Area of the curve rotated about the given line. rotated about the x-axis

y = sin(x)

a = 0 to b = π

rotated about the x-axis

Answer 1

The sum of the circumferences of infinitely many, infinitesimally thin (dx), circles should give us the surface area of this solid. As always, when we integrate a n^th-dimensional quantity (in this case, the 1-d circumference), we get an n+1^st answer (in this case, the 2-d area):

SA = ∫₀^π 2πsinxdx = -2πcosx]₀^π = 4π (Note: the height of the function represents the radius of these circles.)