You have most likely in highschool seen that integrals can be used for the computations of areas and volumes; but these are only a few of the many interpretations and applications of integration. Today we shall integrate functions of two variables over very differently shaped regions in the plane. Or functions of three variables over surfaces in space. NB: It is important that you learn to operate with parametric representation! Using these you can e.g. design your own impressive surfaces in space - if you e.g. will form a new fancy teapot or how about an elegant skyscraper a la ”Turning Torso” in Malmø. If it concerns an otherwise defined given region or surface, you may often have to find your self a suitable parametric representation in order to make computations, e.g. find the area or mass with respect to a mass density function.