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Introduction to Area

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Estimating the area of a circle:

 Area of a Polygon:

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Sums and Sigma Notation

1+2+3+4+...+ 100 =

2+4+6+8+....+ 1000 =

1+4+9+16+....+ 625=

  = Sigma, the capitol Greek letter called "sigma";

It means summation. i   = index

Linearity of

Let denote two sequences and c  is a real number.

(i)

(ii)

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Special Sum Formulas

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EX 1

EX 2

EX 5 Change the variable in the index to start at 1.

i

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Collapsing Sum

EX 3

EX 4

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We will estimate the area under a curve using inscribed or circumscribed rectangles.

EX 6 For f(x)=3x-1, divide the interval [1,3] into 4 equal subintervals.Calculate the area of the circumscribed rectangles.

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