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Sigma Notation

  1. Nov 19, 2011 #1
    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
     

    Attached Files:

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  2. jcsd
  3. Nov 19, 2011 #2

    Dick

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    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.
     
  4. Nov 19, 2011 #3
    I know I could have I just wanted to practice lol..


    .
     
  5. Nov 19, 2011 #4

    Dick

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    That's fine. But there an exact value for the sum. And it isn't 6.85.
     
  6. Nov 20, 2011 #5
    6.875
     
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