\begin{frame}
  \frametitle{Properties of the Definite Integral}

  \begin{exampleblock}{}
    Assume $\int_0^{10} f(x) dx = 17$ and $\int_0^{8} f(x) dx = 12$, find 
    $\int_8^{10} f(x) dx$.
    \pause
    \begin{talign}
      \int_0^{8} \!\!f(x) dx + \int_8^{10} \!\!\!f(x) dx = \int_0^{10} \!\!\!f(x) dx
      \implies \mpause[1]{\int_8^{10} \!\!\!f(x) dx = 17-12=5}
    \end{talign}
  \end{exampleblock}
  \pause\pause
  
  \begin{exampleblock}{}
    Use the properties of integrals to evaluate:
    \begin{talign}
      \int_0^1 (4+3x^2)dx &= \mpause[1]{ \int_0^1 4\;dx + \int_0^1 3x^2 dx} \\
      \mpause{&= 4 + 3\int_0^1 x^2 dx} 
      \mpause{}\\
      \mpause{& = 4 + 3\frac{1}{3} = 5} 
    \end{talign}
    \pause\pause\pause
    We have already seen that
    \begin{talign}
      \int_0^1 x^2dx = \frac{1}{3} 
    \end{talign}
  \end{exampleblock}
\end{frame}