MAT 21B Study Guide - Final Guide: Rhenium, Mean Value Theorem, Improper Integral

• School: UC-Davis
• Department: Mathematics
• Course: MAT 21B
• Professor: Lawrence Marx

Document Summary

Using limits and sum of rhenium sums to find the integral as the partition goes to zero. f(x)dx = lim as llpll -> 0 f(xi) x = f(a+i(b-a/ni) (b-a)/n. I=1 n i = n(n+1)/2 n i2 = n(n+1)(2n+1)/6 n i3 = n2(n+1)2 /4. Mean value theorem if f is continues on [a,b] then there is a number, c, with f(c) = 1/(b-a) b. Extreme value theorem f is continuous so it has a min and a max. Intermediate value theorem f(c) = 1/(b-a) b x f(t)dt = f(x) f(t)dt = f(a) f(b) a f(x)dx for some value in [a,b] a f(x)dx. Area of a plane region between two curves - a top function bottom function dx. Volu(cid:373)e of a solid (cid:449)ho"s (cid:271)ase is (cid:271)ou(cid:374)ded (cid:271)(cid:455) the (cid:396)egio(cid:374)s i(cid:374) the (cid:454)-y plane graph. A (area of the cross section that is made from the base) dx.