Calculating Area of f(x) from 0 to 3 with 6 Rectangles

[Miike012]

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

 

[Dick]

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.

 

[Miike012]

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


.

 

[Dick]

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.

 

[Miike012]

6.875