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Dido525 Group Title

Definition of the definite integral question:

  • one year ago
  • one year ago

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  1. Dido525 Group Title
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    Using the definition of the definite integral, compute: \[\int\limits_{-4}^{2}(3x^2+12x+20)dx\]

    • one year ago
  2. malical Group Title
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    Is the definition of a definition integral FTC or the definition of an integral: lim (x,y)-> (0,0) and on and on?

    • one year ago
  3. jayz657 Group Title
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    take the anti derivative of 3x^2 + 12x + 20 is x^3 +6x + 20x then you plug in 2 and then -4 (2)^3 + 6(2) + 20(2) - [ -4^3 + 12(-4) + 20(-4) ] 8 + 12 + 40 - [ -64 - 48 - 80 ] 60 - [ - 192] = 252

    • one year ago
  4. Dido525 Group Title
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    Definition of integral. @jayz657 Thanks but I want an explanation on this concept.

    • one year ago
  5. Dido525 Group Title
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    I can calculate the anti derivative fine but I have to use Riemann sums @jayz657 .

    • one year ago
  6. Dido525 Group Title
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    Just an explanation of some sort for Riemann sums would be fine. I can do the rest I am sure.

    • one year ago
  7. jayz657 Group Title
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    |dw:1353040377471:dw| this is the riemann sum, you are drawing an infinite amount of rectangles under the curve here you know the length is change of x and the height is f(x) and you sum up each rectangle to get the area under the curve so will will get this \[\sum_{-4}^{2} f(x)\Delta x\]

    • one year ago
  8. Dido525 Group Title
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    Yes I know the fundamental concept. But how would I exactly apply it?

    • one year ago
  9. jayz657 Group Title
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    when you sum up the infinite amount of rectangles you will get the integral there

    • one year ago
  10. malical Group Title
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    You integrate the equation and then you get a function. That function will be in terms of f(x). The top number in the definite integral is b and the lower is a. f(b)-f(a) is your answer. Jayz got 252

    • one year ago
  11. Dido525 Group Title
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    Yeah but How would I exactly sum up an infinite number of rectangles for my given function?

    • one year ago
  12. malical Group Title
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    Do you want to see how to do this problem or the theory behind it?

    • one year ago
  13. Dido525 Group Title
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    @malical : I know how to find an antiderivative. I just have trouble applying riemann sums.

    • one year ago
  14. malical Group Title
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    Why are Riemann sums important?

    • one year ago
  15. Dido525 Group Title
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    The question specifically says to use Riemann sums.

    • one year ago
  16. Dido525 Group Title
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    Never mind. I got it :) .

    • one year ago
  17. jayz657 Group Title
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    the change of x is the rate of change of each rectangle and rate of change is related to the derivative, dx so in this equation you can just draw as many rectangles as you want under the curve using a delta x width and using f(x) as your height heres an exmaple doing it the long way lets say i make 4 rectangles with length 3 |dw:1353040955063:dw|

    • one year ago
  18. Dido525 Group Title
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    Yeah I got it thanks :) .

    • one year ago
  19. jayz657 Group Title
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    ok np

    • one year ago
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