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anonymous

  • one year ago

hey guys hope y"all are well so i have this advance level definite integral question which i have no clue how to slove help , appreciate it :) https://fbcdn-sphotos-f-a.akamaihd.net/hphotos-ak-xfp1/v/t34.0-12/11909631_821736251278657_492814160_n.jpg?oh=3a6369ebefa89e9e8c6cabd375c6fabc&oe=55DC7BCA&__gda__=1440576288_0b59d00ed7b50754e40cf9942f4f8f3f

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  1. freckles
    • one year ago
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    \[\Delta x=\frac{b-a}{N}\] this will be the base length of each rectangle

  2. freckles
    • one year ago
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    you will need to find the height formula... that is the distance from the curve to the x-axis is actually sqrt(x) the height is sqrt(x)

  3. freckles
    • one year ago
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    so starting at left endpoint you would do x=0 x=0+(b-a)/N x=0+2(b-a)/N x=0+3(b-a)/N ... xi=0+i(b-a)/N ... where i=0...35 this will give you 36 rectangles

  4. freckles
    • one year ago
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    right endpoint you would just use i=1..36 instead

  5. anonymous
    • one year ago
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    what is 1..36?

  6. anonymous
    • one year ago
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    oh wait from 1st rectangle to 36th rectangle ?

  7. freckles
    • one year ago
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    \[A_\text{ \left endpoint rule }=\lim_{n \rightarrow \infty} \sum_{i=0}^{35} \Delta x \cdot f(a+i \frac{b-a}{N}) \\ A_{\text{ \right endpoint rule }}=\lim_{n \rightarrow \infty} \sum_{i=1}^{36} \Delta x f(a+i \cdot \frac{b-a}{N})\]

  8. anonymous
    • one year ago
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    thats the answer for a ?

  9. freckles
    • one year ago
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    no

  10. freckles
    • one year ago
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    it can help you get to the answer though

  11. ganeshie8
    • one year ago
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    |dw:1440392239536:dw|

  12. freckles
    • one year ago
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    if you understand it

  13. freckles
    • one year ago
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    lol i did 36 rectangles

  14. freckles
    • one year ago
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    I forgot it said 18

  15. anonymous
    • one year ago
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    See I do understand the definitions nd even can solve the question however I am struggling to understand what this question ultimately asking , I don't understand where U and L fit in the equation SRry about that

  16. anonymous
    • one year ago
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    Yes that's why I was confused why were u doing 36

  17. freckles
    • one year ago
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    i=0..17 i=1..18

  18. freckles
    • one year ago
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    now that will give you 18 rectangles

  19. freckles
    • one year ago
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    use i=0..17 for leftendpoint rule this will start your rectangles from x=0 use i=1..18 for rightendpoint tule this wil start your rectangles from x=0+(b-a)/N

  20. ganeshie8
    • one year ago
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    basically, the problem boils down to finding the area under the curve \(\large f(x)=\sqrt{~x}\) : |dw:1440392648846:dw|

  21. ganeshie8
    • one year ago
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    suppose you don't know calculus or anything, do you have any hope in finding the area of that blue region ?

  22. anonymous
    • one year ago
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    No @ganeshie8

  23. anonymous
    • one year ago
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    Wait unless u know the size of each square

  24. ganeshie8
    • one year ago
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    sure you know the size of each square

  25. ganeshie8
    • one year ago
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    what riemann did is very simple : he divided that area into simple rectangles whose area can be found by simply multiplying width and height

  26. ganeshie8
    • one year ago
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    we will see what U and L mean shortly, but just so you get used to this rectangles business, lets do a quick example maybe ?

  27. anonymous
    • one year ago
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    Sure @ganeshie8

  28. ganeshie8
    • one year ago
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    can you find the area of below two big rectangles ? |dw:1440393131543:dw|

  29. ganeshie8
    • one year ago
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    notice that they both have same width : 18 you will need to find the height of each of them before using area of rectangle formula

  30. anonymous
    • one year ago
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    120unit^2

  31. ganeshie8
    • one year ago
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    how ?

  32. anonymous
    • one year ago
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    90unit^2

  33. anonymous
    • one year ago
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    When I saw the 18 I just did 18times 4

  34. ganeshie8
    • one year ago
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    18 times 4 is 72, not 90

  35. ganeshie8
    • one year ago
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    but from where did u get "4" ?

  36. anonymous
    • one year ago
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    U said area together right ? So (4*9) +(6*9)

  37. anonymous
    • one year ago
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    I just took approximation

  38. ganeshie8
    • one year ago
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    Ahh nice, you have the right idea, but your answer is wrong because the width of each rectangle is 18 |dw:1440393575737:dw|

  39. ganeshie8
    • one year ago
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    it seems you're assuming that the width of each rectangle is just 9, which is wrong..

  40. anonymous
    • one year ago
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    Ok

  41. ganeshie8
    • one year ago
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    try again

  42. anonymous
    • one year ago
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    Can I take the height of each rectangle 4 and 6

  43. ganeshie8
    • one year ago
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    you may, but the exact heights are \(\sqrt{18}\) and \(\sqrt{36}\)

  44. anonymous
    • one year ago
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    (4*18) + (6*16) = 168 unit^2

  45. ganeshie8
    • one year ago
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    looks good! lets do one more exampl

  46. anonymous
    • one year ago
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    Sure

  47. freckles
    • one year ago
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    |dw:1440393845103:dw|