anonymous
  • anonymous
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!!
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
\[\int\limits_{0}^{2} \frac{ x }{ 1+x^2 } dx \]
anonymous
  • anonymous
where n = 10
amistre64
  • amistre64
its finding an approximation to the area under the curve ...

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anonymous
  • anonymous
yes:) how can i set it up? I'm a bit confused with the process :o
amistre64
  • amistre64
instead of left or right values, you are grabbing the value at the middle of the interval
anonymous
  • anonymous
ooh okay! yes:) what do we do to start off?
amistre64
  • amistre64
im not sure how easy it would be to construct the rule .. your material should have it
anonymous
  • anonymous
okay! then, could you please show me how id go about solving this integral?
amistre64
  • amistre64
the hardest part is constructing the rule .. since i dont recall the formula for it off hand. do you have the formula for it?
amistre64
  • amistre64
|dw:1443474213664:dw|
anonymous
  • anonymous
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]
anonymous
  • anonymous
@amistre64 @IrishBoy123 ?
zpupster
  • zpupster
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
amistre64
  • amistre64
powers fluctuating over here ... so my connection isnt stable
anonymous
  • anonymous
okay, i see!!
amistre64
  • amistre64
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
anonymous
  • anonymous
okay!
amistre64
  • amistre64
\[\sum_{i=0}^{n-1}f(\color{red}{a+\frac12\left( i\frac{b-a}{n}+(i+1)\frac{b-a}{n}\right)})\] \[\sum_{i=0}^{n-1}f(\color{red}{a+\frac{b-a}{2n}\left( 2i+1\right)})\] does that seem plausible?
amistre64
  • amistre64
a=0, b=2 sooo \[\sum_{i=0}^{9}f(\color{red}{\frac{2i+1}{10}})\frac1{10}\]
amistre64
  • amistre64
x= 1/10 3/10 5/10 7/10 9/10 11/10 13/10 15/10 17/10 19/10
amistre64
  • amistre64
determine f(x) for each value of x ....
amistre64
  • amistre64
simpsons rule is using a parabolic shape to define the points of reference with.

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