# Sigma Notation

I just read the section so I want to make sure I am doing it correctly..
I am using it to assist in solving an area question....

Question:
Estimate the area under the graph of f(x) = 1 + (x - 1)^2 from x = 0 to x = 3 using 6 rectangles and right end point.

Each rectangle has a base of 0.5 wide

1. Ʃ 1 + (0.5*i - 1)^2 = i^2/4 - i + 2 ; i = 0 and n = 6

2. Breaking them up:

1/4Ʃ i^2 - Ʃ i + Ʃ 2 ; i = 0 and n = 6

3. Calculating the area of f by computing the sum of the areas of each rectangle in
[0 , 3]

.5( 1/4*(6*13*7)/(6) - (6*7)/2 + 6*2) = 6.85

#### Attachments

• sig.png
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## Answers and Replies

Dick
Science Advisor
Homework Helper
You could just do it by adding up the six rectangles and skip the sigma notation altogether. That would probably be simpler. But I think you got it right. Except for the final 6.85 number. That's a little off.

I know I could have I just wanted to practice lol..

.

Dick
Science Advisor
Homework Helper
I know I could have I just wanted to practice lol..

.

That's fine. But there an exact value for the sum. And it isn't 6.85.

6.875