1. The problem statement, all variables and given/known data Find a formal solution to the vibrating string problem.. alpha=4, 0<x<pi t>0 u(0,t)=u(pi,t)=0 t>0 f(x)= x^2(pi-x) g(x)=0 2. Relevant equations u(x,t) = sum[a cos(alpha*n*t/L + b sin(alpha*n*t/L)*sin(n pi x / L) Fourier series for sine 3. The attempt at a solution a = 2/pi * integral(x^2 (pi-x) * sin(nx) dx) from 0 to pi = [-2((n pi)^2 - 2)(-1)^n - 4 + 2((n pi)^2 - 6)(-1)^n] / n^3 ... by breaking it into addition of 2 integrals and using the tabular method of integration b = 2/pi * integral(0 * sin(nx) dx) from 0 to pi = 0 however, the answer is u(x,t) = sum[ 4/n^3 * [2(-1)^(n+1) - 1] * cos2nt sinnx Did I do something wrong or is the answer in a different form? I don't see how to get from my answer to the correct one.