{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# DefInt - Math 21B Kouba Limit Deﬁnition of the Deﬁnite...

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Math 21B Kouba Limit Deﬁnition of the Deﬁnite Integral I.) Consider a function y 2 f (\$) deﬁned on the closed interval [a, b] . 2.) Partition the interval [a, 1)] into n pieces of any size : \$0 : CL, 3713 \$23 \$39' ' '7 3:11—11 b : \$17, Deﬁne the mesh of the partition to be 2 1{page (x, — \$,_1) . (In other words, the mesh __Z__n of a partition is the length of the largest subinterval.) X0: 4 X1 X1 X3 X9 ‘ " XVI—2. Xn-i I0: Xn C4 C1 C3 ‘1‘! ' ' ' ch—( ch 3.) Pick sampling points c1, (:2, 03,--~, cn_1, en , where c, is a number in the subinterval [:v,_1, 33,] for i = 1,2,3, - --,n . Let Am,- 2 x,- — mi_1 be the length of the subinterval [ml-4, 27,] for 2' = 1,2,3, ~ ~ ',n . n 4.) Compute the Riemann Sum deﬁned by Zf(c,-) ' Aw,- i=1 5.) The Deﬁnite Integral is then given to be b n t f<w> dw=mgnogf<w>ewi REMARK : The above is a formal and general deﬁnition of the Deﬁnite Integral. When 6 doing problems using this step-by-step process for computing / f (:L') d1: , it is convenient to i.) pick equally-spaced partition points so that all of the subintervals have the same b — a length: Ami: fori:1,2,3,---,n; n ii.) pick sampling points to be the right—hand endpoints of the subintervals : b —— a -2' fori:1,2,3,-~,n;then n b n n / f(:l}) d1: = lim Zﬂcz) - A33,- : "1320 Zﬂci) - A33, . (1 i=1 0,- = a + iii.) mesh—)0 . 1,:1 ...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern