# Thread: Calculus problem with lengths of curves

1. ## Calculus problem with lengths of curves

Let L be the length of the curve y = f(x), q </= x </= u, where f is positibe and has a continuous derivative. Let Sf be the surface area generated by rotating the curve about the x-axis. If c is a positive constant, define g(x) = f(x) + c and let Sg be the corresponding surface area generated by the curve y = g(x), q </= x </= u. Express Sg in terms of Sf and L.

I can't get it. It's a homework problem!

2. Originally Posted by jamessmith
Let L be the length of the curve y = f(x), q </= x </= u, where f is positibe and has a continuous derivative. Let Sf be the surface area generated by rotating the curve about the x-axis. If c is a positive constant, define g(x) = f(x) + c and let Sg be the corresponding surface area generated by the curve y = g(x), q </= x </= u. Express Sg in terms of Sf and L.

I can't get it. It's a homework problem!
$S_g=2\pi \int_q^u g(x) \ ds=2\pi \int_q^u f(x) \ ds + 2 \pi \int_q^u c \ ds=S_f + 2\pi c L.$