Posted on September 16, 2021October 24, 2022 by 202109161055 Exercises 3.3.A (Q1) For Exercises 1-8, evaluate the given triple integral. Solution.
![\begin{aligned} & \qquad \int_{0}^{3}\int_{0}^{2}\int_{0}^{1}xyz\,\mathrm{d}x\,\mathrm{d}y\,\mathrm{d}z \\ & = \int_{0}^{3}\int_{0}^{2} \bigg(\frac{x^2yz}{2}\bigg|_{x=0}^{x=1}\bigg)\,\mathrm{d}y\,\mathrm{d}z \\ & = \int_{0}^{3}\int_{0}^{2}\bigg(\frac{yz}{2}\bigg)\,\mathrm{d}y\,\mathrm{d}z \\ & = \int_{0}^{3}\bigg( \frac{y^2z}{4}\bigg|_{y=0}^{y=2} \bigg) \,\mathrm{d}z \\ & = \int_{0}^{3} z\,\mathrm{d}z \\ & = \bigg[\frac{z^2}{2}\bigg]_{0}^{3} \\ & = 4\frac{1}{2} \\ \end{aligned}](https://physicspupil.com/wp-content/ql-cache/quicklatex.com-73a9a99dffed3134dd8c75fb87dea5aa_l3.svg "Rendered by QuickLaTeX.com")
