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Triple Integrals
https://math.libretexts.org/Courses/Montana_State_University/M273%3A_Multivariable_Calculus/15%3A_Multiple_Integration/Triple_Integrals
\[\begin{align*} \int_{x=0}^{x=1} \int_{y=0}^{y=x^2} \int_{z=0}^{z=y^2} xyz \, dz \, dy \, dx \\ = \int_{x=0}^{x=1} \int_{y=0}^{y=x^2} \left. \left[xy \dfrac{z^2}{2} \right|_{z=0}^{z=y^2} \right] \, d... $\begin{align*} \int_{x=0}^{x=1} \int_{y=0}^{y=x^2} \int_{z=0}^{z=y^2} xyz \, dz \, dy \, dx \\ = \int_{x=0}^{x=1} \int_{y=0}^{y=x^2} \left. \left[xy \dfrac{z^2}{2} \right|_{z=0}^{z=y^2} \right] \, dy \, dx = \int_{x=0}^{x=1} \int_{y=0}^{y=x^2} \left( x \dfrac{y^5}{2}\right) dy \, dx = \int_{x=0}^{x=1} \left. \left[ x\dfrac{y^6}{12} \right|_{y=0}^{y=x^2}\right] dx = \int_{x=0}^{x=1} \dfrac{x^{13}}{12} dx = \left. \dfrac{x^{14}}{168}\right|_{x=0}^{x=1} = \dfrac{1}{168}, \end{align*}$
Triple Integrals
https://math.libretexts.org/Courses/Georgia_State_University_-_Perimeter_College/MATH_2215%3A_Calculus_III/15%3A_Multiple_Integration/Triple_Integrals
\[\begin{align*} \int_{x=0}^{x=1} \int_{y=0}^{y=x^2} \int_{z=0}^{z=y^2} xyz \, dz \, dy \, dx \\ = \int_{x=0}^{x=1} \int_{y=0}^{y=x^2} \left. \left[xy \dfrac{z^2}{2} \right|_{z=0}^{z=y^2} \right] \, d... $\begin{align*} \int_{x=0}^{x=1} \int_{y=0}^{y=x^2} \int_{z=0}^{z=y^2} xyz \, dz \, dy \, dx \\ = \int_{x=0}^{x=1} \int_{y=0}^{y=x^2} \left. \left[xy \dfrac{z^2}{2} \right|_{z=0}^{z=y^2} \right] \, dy \, dx = \int_{x=0}^{x=1} \int_{y=0}^{y=x^2} \left( x \dfrac{y^5}{2}\right) dy \, dx = \int_{x=0}^{x=1} \left. \left[ x\dfrac{y^6}{12} \right|_{y=0}^{y=x^2}\right] dx = \int_{x=0}^{x=1} \dfrac{x^{13}}{12} dx = \left. \dfrac{x^{14}}{168}\right|_{x=0}^{x=1} = \dfrac{1}{168}, \end{align*}$
4.10: Triple Integrals
https://math.libretexts.org/Courses/Misericordia_University/MTH_226%3A_Calculus_III/Chapter_15%3A_Multiple_Integration/4.10%3A_Triple_Integrals
\[\begin{align*} \int_{x=0}^{x=1} \int_{y=0}^{y=x^2} \int_{z=0}^{z=y^2} xyz \, dz \, dy \, dx \\ = \int_{x=0}^{x=1} \int_{y=0}^{y=x^2} \left. \left[xy \dfrac{z^2}{2} \right|_{z=0}^{z=y^2} \right] \, d... $\begin{align*} \int_{x=0}^{x=1} \int_{y=0}^{y=x^2} \int_{z=0}^{z=y^2} xyz \, dz \, dy \, dx \\ = \int_{x=0}^{x=1} \int_{y=0}^{y=x^2} \left. \left[xy \dfrac{z^2}{2} \right|_{z=0}^{z=y^2} \right] \, dy \, dx = \int_{x=0}^{x=1} \int_{y=0}^{y=x^2} \left( x \dfrac{y^5}{2}\right) dy \, dx = \int_{x=0}^{x=1} \left. \left[ x\dfrac{y^6}{12} \right|_{y=0}^{y=x^2}\right] dx = \int_{x=0}^{x=1} \dfrac{x^{13}}{12} dx = \left. \dfrac{x^{14}}{168}\right|_{x=0}^{x=1} = \dfrac{1}{168}, \end{align*}$

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