\begin{frame} \frametitle{Fundamental Theorem of Calculus} \fundamental \medskip \begin{exampleblock}{} Find the area under $\cos x$ from $0$ to $b$ where $0\le b \le \pi/2$. \pause\medskip For $0 \le x \le \pi/2$, we have $\cos x \ge 0$. \pause Thus area = integral. \pause\medskip An antiderivative of $f(x) = \cos x$ is $F(x) = \pause \sin x$. \pause Then \begin{talign} \int_0^b \cos x\;dx = \mpause[1]{\sin x \big]_0^b} \mpause{= \sin b - \sin 0} \mpause{= \sin b} \end{talign} \end{exampleblock} \vspace{10cm} \end{frame}