\begin{frame} \frametitle{Fundamental Theorem of Calculus} \fundamental \medskip \begin{exampleblock}{} Find the area under the parabola \begin{talign} f(x) = x^2 \end{talign} from $0$ to $1$. \pause\medskip From $0$ to $1$ the curve is above the $x$-axis. \pause Thus area = integral. \pause\medskip An antiderivative of $f$ is $F(x) = \pause \frac{1}{3}x^3$. \pause\medskip By the Fundamental Theorem, the area is: \begin{talign} A = \int_0^1 x^2 \, dx= \mpause[1]{\frac{1}{3}x^3 \Big]_0^1} \mpause{= \frac{1}{3}1^3 - \frac{1}{3}0^3} \mpause{= \frac{1}{3}} \end{talign} \end{exampleblock} \vspace{10cm} \end{frame}