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anonymous

  • one year ago

How do I solve this integral using a) the midpoint rule and b) simp son's rule to approximate the integral? can you please explain? thank you!!

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  1. anonymous
    • one year ago
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    \[\int\limits_{0}^{2} \frac{ x }{ 1+x^2 } dx \]

  2. anonymous
    • one year ago
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    where n = 10

  3. amistre64
    • one year ago
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    its finding an approximation to the area under the curve ...

  4. anonymous
    • one year ago
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    yes:) how can i set it up? I'm a bit confused with the process :o

  5. amistre64
    • one year ago
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    instead of left or right values, you are grabbing the value at the middle of the interval

  6. anonymous
    • one year ago
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    ooh okay! yes:) what do we do to start off?

  7. amistre64
    • one year ago
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    im not sure how easy it would be to construct the rule .. your material should have it

  8. anonymous
    • one year ago
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    okay! then, could you please show me how id go about solving this integral?

  9. amistre64
    • one year ago
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    the hardest part is constructing the rule .. since i dont recall the formula for it off hand. do you have the formula for it?

  10. amistre64
    • one year ago
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    |dw:1443474213664:dw|

  11. anonymous
    • one year ago
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    yes! it is this for midpoint rule integral of a to b f(x) dx is approximately M_n = delta x [f(x1)+f(x2)+….+f(xn)] where delta x = b-a / n and xi=1/2(xi-1 + xi) = midpoint of [xi-1, xi]

  12. anonymous
    • one year ago
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    @amistre64 @IrishBoy123 ?

  13. zpupster
    • one year ago
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    i never heard of this but i watched this video and I understand it but it is a lot of work https://www.youtube.com/watch?v=fKtSR0_xf5g

  14. amistre64
    • one year ago
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    powers fluctuating over here ... so my connection isnt stable

  15. anonymous
    • one year ago
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    okay, i see!!

  16. amistre64
    • one year ago
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    f (a + ((i_n)dx+(i_(n+1)dx)/2 ) f (a + ((i_n)+(i_(n+1)) dx/2 ) , for i from a to n-1

  17. anonymous
    • one year ago
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    okay!

  18. amistre64
    • one year ago
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    \[\sum_{i=0}^{n-1}f(\color{red}{a+\frac12\left( i\frac{b-a}{n}+(i+1)\frac{b-a}{n}\right)})\] \[\sum_{i=0}^{n-1}f(\color{red}{a+\frac{b-a}{2n}\left( 2i+1\right)})\] does that seem plausible?

  19. amistre64
    • one year ago
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    a=0, b=2 sooo \[\sum_{i=0}^{9}f(\color{red}{\frac{2i+1}{10}})\frac1{10}\]

  20. amistre64
    • one year ago
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    x= 1/10 3/10 5/10 7/10 9/10 11/10 13/10 15/10 17/10 19/10

  21. amistre64
    • one year ago
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    determine f(x) for each value of x ....

  22. amistre64
    • one year ago
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    simpsons rule is using a parabolic shape to define the points of reference with.

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