@Article{JMS-50-268, author = {Shibo and Liu and liusb@xmu.edu.cn and 7077 and Department of Mathematics, Xiamen University, Xiamen 361005, P.R. China and Shibo Liu and Yashan and Zhang and colourful2009@163.com and 7078 and Department of Mathematics, University of Macau, Macau, P.R. China and Yashan Zhang}, title = {On the Change of Variables Formula for Multiple Integrals}, journal = {Journal of Mathematical Study}, year = {2017}, volume = {50}, number = {3}, pages = {268--276}, abstract = {

We develop an elementary proof of the change of variables formula in multiple integrals. Our proof is based on an induction argument. Assuming the formula for $(m-1)$-integrals, we define the integral over hypersurface in $\mathbb{R}^m$, establish the divergent theorem and then use the divergent theorem to prove the formula for $m$-integrals. In addition to its simplicity, an advantage of our approach is that it yields the Brouwer Fixed Point Theorem as a corollary.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v50n3.17.04}, url = {http://global-sci.org/intro/article_detail/jms/10620.html} }