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...Multiple integrals exercises with solutions laurenz wiskott institut fur neuroinformatik ruhr universit at bochum germany eu february contents introduction calculating exercise integral of a function between two curves changing the order integration in opposite coordinate system jacobian determinant nonlinear transformation variable area gauss theorem by parts dimensions laurenzwiskott orcidhttp orcid org x homepagehttps www ini rub de people this work except for all gures from other sources if present is licensed under creative commons attribution sharealike international license see http creativecommons licenses sa these complement my corresponding lecture notes and there version one without table reproduced here to give an orientation when can be reasonably solved best learning eect i recommend rst seriously try solve yourself before looking into more teaching material available https integrate f y xy over region solution has bit careful sketching functions shows that thus we have s...