Abstract
In Sect. 11.3 we have shown how to calculate the volume of solids of revolution. If there is no rotational symmetry, however, one needs an extension of integral calculus to functions of two variables. This arises, for example, if one wants to find the volume of a solid that lies between a domain D in the (x, y)-plane and the graph of a non-negative function \(z = f(x, y)\). In this section we will extend the notion of Riemann integrals from Chap. 11 to double integrals of functions of two variables. Important tools for the computation of double integrals are their representation as iterated integrals and the transformation formula (change of coordinates). The integration of functions of several variables occurs in numerous applications, a few of which we will discuss.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
