Problem with integrating sine function I have a problem solving an integration. This is my approach:
\begin{align*}
u &= \frac{1}{T}\cdot\intop_{0}^{T}(U_{0}+\hat{u}\cdot \sin(\omega t))dt\qquad\text{with }\omega=\frac{2\pi}{T}\\
u &= \frac{1}{T}\cdot\intop_{0}^{T}(U_{0}+\hat{u}\cdot \sin(\frac{2\pi}{T}\cdot t))dt\\
u &= \frac{1}{T}\cdot\left[U_{0}t-\hat{u}\cdot\frac{T}{2\pi}\cdot\cos\frac{2\pi}{T}\cdot t\right]_{0}^{T}\\
u &= \frac{U_{0}T}{T}-\hat{u}\cdot\frac{T}{2\pi\cdot T}\cdot\cos\frac{2\pi\cdot T}{T}\\
u &= U_{0}-\hat{u}\cdot\frac{1}{2\pi}\cdot\cos2\pi\\
u &= U_{0}-\frac{\hat{u}}{2\pi}.
\end{align*}
But the solution should be ${u = U_{0}}$. Where is my mistake?

It's $\cos 0=1$, not $\cos 0=0$.
