{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# Calc05_2 - 5.2 Definite Integrals Greg Kelly Hanford High...

This preview shows pages 1–6. Sign up to view the full content.

5.2 Definite Integrals Greg Kelly, Hanford High School, Richland, Washington

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
When we find the area under a curve by adding rectangles, the answer is called a Rieman sum . 2 1 1 8 V t = + subinterval partition The width of a rectangle is called a subinterval . The entire interval is called the partition . Subintervals do not all have to be the same size.
2 1 1 8 V t = + subinterval partition If the partition is denoted by P , then the length of the longest subinterval is called the norm of P and is denoted by . P As gets smaller, the approximation for the area gets better. P ( 29 0 1 Area lim n k k P k f c x = = if P is a partition of the interval [ ] , a b

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
( 29 0 1 lim n k k P k f c x = is called the definite integral of over . f [ ] , a b If we use subintervals of equal length, then the length of a subinterval is: b a x n - = The definite integral is then given by: ( 29 1 lim n k n k f c x →∞ =
( 29 1 lim n k n k f c x →∞ = Leibnitz introduced a simpler notation for the definite integral: ( 29 ( 29 1 lim n b k a n k f c x f x dx →∞ = = Note that the very small change in x becomes dx .

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the 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