MATH 2400 Lecture Notes - Lecture 12: Riemann Sum, Multiple Integral, Contour Line
22 Apr 2019
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12. 1 double integrals over rectangles -- math 2400 sec 006/011/013, fall 2018. Review of riemann sum, area and definite integral: if f(x) is defined on as x sb, we divide the interval [a, b] into n subintervals [x1_1, x1] of equal width l:i. x = ~ -xi e [x,_1, x ;]. Then the limit of riemann sum is the definite integral from a to b (we assume the limit exists) Volumes and double integrals: consider a function f of two variables defined on closed rectangle. Let s be the solid that lies above rand under the graph off (f(x, y) ~ o), that is, S = {(x, y, z) e r3 i os z s f(x, y), (x, y) e r} h. Then the volume of the solid s is lim f f. f(x1j,,n)t:. x n l l / l. The double integral off over "the rectangle r is.
