unimatix
  • unimatix
Prove that both trapezoid rule and Simpson's rule give an estimate within 0.005 of true value of integral?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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unimatix
  • unimatix
Using Maple I've found: trapezoid rule gives 2.432066146 Simpson's rule gives 2.430797145
unimatix
  • unimatix
\[\int\limits_{a}^{b}\frac{ x^2 }{ \sqrt{(1-x^2)(k^2-x^2)} }\] a = 3 b = 5 k = 2
unimatix
  • unimatix
@SolomonZelman @pooja195

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unimatix
  • unimatix
Even if someone just has an idea that might be helpful.
dan815
  • dan815
error bound on simpsons rule
anonymous
  • anonymous
you want to confirm this numerically or you want to prove it using the error bound theorem
dan815
  • dan815
i think to find error bounds for trapezoidal one
dan815
  • dan815
take all right end points and all left end points
dan815
  • dan815
the true value is between those 2 answers
dan815
  • dan815
if you show that the difference between trap right end points trap left end points method is less than 0.005 then your answer is within 0.005 of the true value
unimatix
  • unimatix
Okay thanks I'll try and see if I can figure out how to do that.
dan815
  • dan815
I am not completely sure about this argument though
dan815
  • dan815
it could be possible that both the right end points and the left end points are both greater than the true value, or both less than the true value
dan815
  • dan815
yeah throw that method out of the window, there is a more mathematical way
dan815
  • dan815
https://www.youtube.com/watch?v=qVXIU6mKank This tells you about simpsons error bound
unimatix
  • unimatix
Hah that's funny I just found that. I don't see one for the Trapezoid rule though :-/
dan815
  • dan815
isnt simpsons just a higher order trap
unimatix
  • unimatix
I don't really know what that means.
dan815
  • dan815
simpsons rule is just like beight a bit smarter about the trapezoidal rule
dan815
  • dan815
it will take the average of the areas of the trapezoids in a smarter way
unimatix
  • unimatix
Okay. So it will be found in a similar way?
dan815
  • dan815
yeah u should understand the pictures of these operations that will make it a lot clearer
dan815
  • dan815
https://www.youtube.com/watch?v=uc4xJsi99bk
dan815
  • dan815
ok i see now
dan815
  • dan815
basically for trapezoidal
dan815
  • dan815
|dw:1442549451279:dw|
dan815
  • dan815
|dw:1442549479549:dw|
dan815
  • dan815
we went from line connections to parabollic connections
dan815
  • dan815
for trap to simpsons
dan815
  • dan815
u can keep going on in this way
dan815
  • dan815
like higher order simpsons rule, instead of parabola u can do x^3 , x^4,x^5 curve connections
unimatix
  • unimatix
Okay that makes sense

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