{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

The Fundamental Theorem of Calculus

# The Fundamental Theorem of Calculus - i n i n Left F...

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

The Fundamental Theorem of Calculus (Part2) dx x f b a ) ( = F(b) – F(a) where F’(x) = f (x) Proof: In the beginning, we established that integration is the sum of the area under the curve. We used Reimann sums to define integrals: dx x f b a ) ( = n lim i n i i x x f = 1 ) ( = n lim i i i x x F = ) ( ' ASIDE Since i x is an unknown coordinate between Left i and Right i , we could name it ‘c’ that satisfies the MVT for F(x) in the interval Δ i x . = n lim i n i x c F = 1 ) ( ' = i i i i n i n x x Left F Right F - = →∞ ) ( ) ( lim 1 = ) ( ) (
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: i n i n Left F Right-∑ = →∞ = ) ( ) ( ... ) ( ) ( ) ( ) ( lim 2 2 1 1 1 n n n i n Left F Right F Left F Right F Left F Right F-+ +-+-∑ = →∞ = ) ( ) ( ... ) ( ) ( ) ( ) ( lim 2 2 1 n n Left F b F Left F Right F a F Right F-+ +-+-→∞ = ) ( ) ( b F a F +-= ) ( ) ( a F b F-The limit drops because the limit of the constant is the constant F(R n ) = F(b) a = Left 1 F(L 1 ) = F(a) b = Right n y = F(x)...
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