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Study23 Group Title

RHS HELP!!! (Reimann Sums) (Note that I have NOT learned about integrals yet) Here's the Q: I'm given a curve where 0<=x<=10, and there are 5 rectangles, so n=5. I calculated delta x to be 2. I'm really confused how to use these two formulas to find both the LHS and the RHS. I've typed the two formulas below, in my reply. Please help!! I AM REALLY CONFUSED! Thank you!

  • one year ago
  • one year ago

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  1. Study23 Group Title
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    \[\ \huge \text {LHS:} \sum_{i=0}^{n-1} f(x_i) Δ x \]

    • one year ago
  2. Study23 Group Title
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    \[\ \ \huge \text {RHS:} \sum_{i=1}^{n} f(x_i) Δ x \]

    • one year ago
  3. hamza_b23 Group Title
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    well delta x = (b-a)/n

    • one year ago
  4. hamza_b23 Group Title
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    and what is your f(x)?

    • one year ago
  5. khoala4pham Group Title
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    I'm not sure what you're asking. I need your function value.

    • one year ago
  6. Study23 Group Title
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    \(\ \Huge \text{Oh, and: } x_i = a+iΔx \)

    • one year ago
  7. hamza_b23 Group Title
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    if you just started integrals you shouldve went over sigma notation im pretty sure, and you just expand it

    • one year ago
  8. khoala4pham Group Title
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    This isn't helpful without the function. Otherwise the answer will be just theoretical stuff.

    • one year ago
  9. Study23 Group Title
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    I don't have a function value... I'm only given a graph in my textbook and am told to find the lower estimate and an upper estimate.

    • one year ago
  10. Study23 Group Title
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    And, we haven't even discussed what an integral is in class...

    • one year ago
  11. khoala4pham Group Title
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    Could you give a description of what your graph is?

    • one year ago
  12. Study23 Group Title
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    It looks something like:|dw:1360464858577:dw|

    • one year ago
  13. Study23 Group Title
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    My confusion is I'm not sure how to use the two summation equations....

    • one year ago
  14. Study23 Group Title
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    And then use the values I know from the graph

    • one year ago
  15. khoala4pham Group Title
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    Okay, that's better. Well you first need to partition the interval into 5 equal intervals. For the left Riemann: for your values x = 0,2,4,6,8, draw a vertical line that TOUCHES the graph of the function. This vertical line is the height of the rectangle that you are estimating the curve with. Each rectangle's width is 2. |dw:1360465074815:dw| For the right hand do the same except for now, use let the x values be x = 2,4,6,8,10 |dw:1360465192357:dw|

    • one year ago
  16. khoala4pham Group Title
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    Note how the left hand Riemann is an underestimation of area while the right hand Riemann is an over estimation of area.

    • one year ago
  17. Study23 Group Title
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    @khoala4pham How do I use the sigma equations? Where do they come into this?

    • one year ago
  18. Study23 Group Title
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    Anyone??

    • one year ago
  19. khoala4pham Group Title
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    The sigma equations represent area. They mean that you sum up the areas of each individual rectangle. That is all that they mean. For the left hand Riemann, you take 2*(f(0) + f(2) + f(4) + f(6) + f(8)) For the right, 2*(f(2) + f(4) + f(6) + f(8) + f(10)) Why that though? Because for the RHR, the first rectangle has height f(0) and its width is 2. The second rectangle has height f(2) and width 2. So forth and so on.

    • one year ago
  20. Study23 Group Title
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    How do you know to choose 0,2,4,6,8 and 2,4,6,8,10?

    • one year ago
  21. khoala4pham Group Title
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    Well your a is zero in this case. a is the place where your interval begins. From your equation of the left hand Riemann, you see that x_i = a + i*(deltax) i runs from 0 to n-1. Well, n here is 5--the domain is partitioned into 5 intervals. That means that i = 0,1,2,3,4. Consequently x will be x = 0 + 2(0), 0 + 2(1), 0+2(2),0+2(3),0+2(4) x = 0,2,4,6,8. The same applies to the right Riemann.

    • one year ago
  22. Study23 Group Title
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    THAT MAKES SO MUCH MORE SENSE! THANK YOU, @khoala4pham! I was getting confused with the \(\ \Huge \sum \text{ notation!} \)

    • one year ago
  23. khoala4pham Group Title
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    The notation is highly ambiguous if you are not used to it. The x_i is a number. Deltax is also a number. You are summing numbers across indexes. How you found your index is obtained above.

    • one year ago
  24. Study23 Group Title
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    Can you explain the RHS for "Well your a is zero in this case. a is the place where your interval begins. From your equation of the left hand Riemann, you see that x_i = a + i*(deltax) i runs from 0 to n-1. Well, n here is 5--the domain is partitioned into 5 intervals. That means that i = 0,1,2,3,4. Consequently x will be x = 0 + 2(0), 0 + 2(1), 0+2(2),0+2(3),0+2(4) x = 0,2,4,6,8. The same applies to the right Riemann." I dont really understand the RHS...

    • one year ago
  25. Study23 Group Title
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    How you got the numbers 2,4,6,8,10

    • one year ago
  26. Study23 Group Title
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    If i runs from 1 to n, so that means i runs 1 to 5...

    • one year ago
  27. Study23 Group Title
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    I'm getting like 2, 5 ...? x_1= (a=0) + (1)(delta x = 2) = 2 x_2 = (a=1) + (2)( delta x = 2) =5

    • one year ago
  28. Study23 Group Title
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    @khoala4pham Why do you keep 0 constant? Consequently x will be x = 0 + 2(0), 0 + 2(1), 0+2(2),0+2(3),0+2(4) x = 0,2,4,6,8.

    • one year ago
  29. khoala4pham Group Title
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    your equation of x_i = a + i*(delta x). a = 0 by default. a is the value that you start your interval with. if your interval were from (20,50) then a = 20. If your interval were (-3,24), then a = -3. In your initial problem you told me that 0 <= x < = 10. Thus a = 0.

    • one year ago
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