5.3 The Fundamental Theorem of Calculus/25: Difference between revisions
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<math> | <math> | ||
\begin{align} | \begin{align} | ||
\end{align} | |||
</math> | |||
\int_{1}^{2}\left(\frac{3}{t^4}\right)dt = \int_{1}^{2}\left(\{3t^-4}\right) \\ | \int_{1}^{2}\left(\frac{3}{t^4}\right)dt = \int_{1}^{2}\left(\{3t^-4}\right) \\ | ||
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&= 1+\frac{-1}{8} = \frac{7}{8} | &= 1+\frac{-1}{8} = \frac{7}{8} | ||
Revision as of 19:58, 25 August 2022
\int_{1}^{2}\left(\frac{3}{t^4}\right)dt = \int_{1}^{2}\left(\{3t^-4}\right) \\
&= \frac{3t^-4}{-3}\bigg|_{1}^{2} = -t^-3 \bigg|_{1}^{2} \\
&= \left[-(2)^-3\right]-\left[-(1)^-3\right] \\[2ex]
&= 1+\frac{-1}{8} = \frac{7}{8}