Chapter 5.1 - Area and Distance

Question 1

What are some Area equations?

Answer 1

Rn = (n+1)(2n+1)/ln^2
A = lim(n->∞)Rn = lim(n->∞)Ln
Δx = b -a/n 
Rn = f(x1) Δx + f(x2) Δx + ... + f(xn) Δx

Question 2

What is the definition of area?

Answer 2

The area of the region S that lies under the graph of the continuous function f is the limit F the sum of the areas of approximating rectangles

Question 3

What is the equation for Reimman Sum

Answer 3

A = lim(n->∞)Rn = lim(n->∞) [f(x1)Δx + f(x2)Δx +…+ f(xn)Δx]
we often use sigma notation to write sums with many terms more compactly. For instance

Σ(i =1)

Question 4

The sigma notation equation for Reimman Sum of i^2 is what?

Answer 4

Σ(i=1) i^2 = n(n+1)(2n+1)/6