# L24 - Lecture 24 Area and Distance Accumulated Change...

This preview shows pages 1–4. Sign up to view the full content.

Lecture 24 — Area and Distance, Accumulated Change, Riemann Sums We used derivatives to solve problems involving rates of change. The second application of calculus is the problem of area and its interpretations. Once again, we will need limits. Find the area beneath the graph of the function f ( x ) = x 2 on the interval [ 0 , 1 ] : Let R n be the sum of the areas of n approximating rectangles each of equal width and height When n = 4 : R 4 =

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

View Full Document
When n = 8 : R 8 = In general, R n = Looking at the graph, the approximations in this problem are closer and closer to the actual area each time, but are always By the completeness axiom, the numbers R n have which must be lim n →∞ R n = so we deﬁne the area to be
In general, given a function f ( x ) , divide [ a,b ] into n subintervals using the partition a = = b This creates the n subintervals: on which we’ll make n rectangles, each having: width Δ x i = height f ( x * i ) , where x * i The sum of these n rectangles is called a Riemann Sum and is written: or, in sigma notation:

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.

## This note was uploaded on 05/27/2011 for the course MAC 2311 taught by Professor All during the Spring '08 term at University of Florida.

### Page1 / 10

L24 - Lecture 24 Area and Distance Accumulated Change...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online