5.3 The Fundamental Theorem of Calculus/41: Difference between revisions
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<math> = \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 = -\cos(x)\bigg|_{0}^{\frac{\pi}{2}} + \sin(x)\bigg|_{\frac{\pi}{2}}^{\pi} | <math> = \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 = -\cos(x)\bigg|_{0}^{\frac{\pi}{2}} + \sin(x)\bigg|_{\frac{\pi}{2}}^{\pi} = -\cos(\frac{\pi}{2}) | ||
</math> | </math> | ||
Revision as of 19:03, 26 August 2022
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 \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} }
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 = \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 = -\cos(x)\bigg|_{0}^{\frac{\pi}{2}} + \sin(x)\bigg|_{\frac{\pi}{2}}^{\pi} = -\cos(\frac{\pi}{2}) }