MATH 323 Lecture Notes - Riemann Sum, Iterated Integral, Multiple Integral
23 Apr 2014
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Document Summary
In calculus of a single variable the de nite integral for f(x)>=0 is the area under the curve f(x) from x=a to x=b. For general f(x) the de nite integral is equal to the area above the x-axis minus the area below the x-axis. The de nite integral can be extended to functions of more than one variable. The de nite integral is denoted by where r is the region of integration in the xy-plane. For positive f(x,y), the de nite integral is equal to the volume under the surface z=f(x,y) and above xy-plane for x and y in the region r. this is shown in the gure below. For general f(x,y), the de nite integral is equal to the volume above the xy-plane minus the volume below the xy-plane. Double integrals arise in a number of areas of science and engineering, including computations of.
