5.5 The Substitution Rule/15: Difference between revisions
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<math>\begin{align}\int sin \pi t dt \end{align} | <math>\begin{align} \ \int sin(\pi t) dt | ||
\end{align} | |||
</math> | |||
<math> | |||
\begin{align} | |||
let \; u &=\pi t \\[2ex] | |||
du &= \pi\; dx \\[2ex] | |||
\frac{1}{\pi}du &= dx | |||
\end{align} | |||
</math> | |||
<math>\begin{align} \ \int sin(\pi t) dt = \int sin(u)(\frac{1}{\pi}du)= \int \frac{1}{\pi} (-cosu) + c = \int - \frac{1}{\pi} cos (\pi t) + c | |||
\end{align} | |||
</math> | </math> | ||
Latest revision as of 05:37, 5 September 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 \begin{align} \ \int sin(\pi t) dt \end{align} }
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} let \; u &=\pi t \\[2ex] du &= \pi\; dx \\[2ex] \frac{1}{\pi}du &= dx \end{align} }
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 sin(\pi t) dt = \int sin(u)(\frac{1}{\pi}du)= \int \frac{1}{\pi} (-cosu) + c = \int - \frac{1}{\pi} cos (\pi t) + c \end{align} }