5.3 The Fundamental Theorem of Calculus/25

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_{1}^{2}\left(\frac{3}{t^4}\right)dt &= \int_{1}^{2}\left(3t^{-4}\right)\,dt \\[2ex] &= \frac{3t^{-4+1}}{-4+1}\bigg|_{1}^{2} = -t^{-3} \bigg|_{1}^{2} \\[2ex] &= \left[-(2)^{-3}\right]-\left[-(1)^{-3}\right] \\[2ex] &= \left[-\frac{1}{8}\right]+[1] = \frac{7}{8} \end{align} }