5.5 The Substitution Rule/55: Difference between revisions
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\int_{0}^{\pi} \sec^2\left(\frac{t}{4}\right)dt | \int_{0}^{\pi} \sec^2\left(\frac{t}{4}\right)dt | ||
&= 4\int_{0}^{\pi} \sec^2(u)du \\[2ex] | |||
\end{align} | \end{align} | ||
Revision as of 16:12, 4 October 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_{0}^{\pi} \sec^2\left(\frac{t}{4}\right)dt }
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} u &= \frac{t}{4} \\[2ex] du &= \frac{1}{4}dt \\[2ex] 4du &=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_{0}^{\pi} \sec^2\left(\frac{t}{4}\right)dt &= 4\int_{0}^{\pi} \sec^2(u)du \\[2ex] \end{align} }
= 4\cdot \tan^2(u) &= 4\int_{0}^{\pi} \sec^2(u)du \\[2ex]