5.3 The Fundamental Theorem of Calculus/41

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \begin{align} \int\limits_{0}^{\pi}f(x)dx \quad \text{where} \; f(x) = \begin{cases} sin(x) & 0 \le x < \frac{\pi}{2} \\ cos(x) & \frac{\pi}{2} \le x \le \pi \end{cases} &= \int\limits_{0}^{\frac{\pi}{2}}f(x)dx + \int\limits_{\frac{\pi}{2}}^{\pi}f(x)dx = \int\limits_{0}^{\frac{\pi}{2}}\sin(x)dx + \int\limits_{\frac{\pi}{2}}^{\pi}\cos(x)dx \\[2ex] &= -\cos(x)\\[2ex] \end{align} }