∫ 1 2 ( 3 t 4 ) d t = ∫ 1 2 ( 3 t − 4 ) d t = 3 t − 4 + 1 − 4 + 1 | 1 2 = − t − 3 | 1 2 = [ − ( 2 ) − 3 ] − [ − ( 1 ) − 3 ] = [ − 1 8 ] + [ 1 ] = 7 8 {\displaystyle {\begin{aligned}\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{aligned}}}
![{\displaystyle {\begin{aligned}\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{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/a17338f8b3b287bbf56443dbf56ea5bf932081bd)