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unimatix
 one year ago
Prove that both trapezoid rule and Simpson's rule give an estimate within 0.005 of true value of integral?
unimatix
 one year ago
Prove that both trapezoid rule and Simpson's rule give an estimate within 0.005 of true value of integral?

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unimatix
 one year ago
Best ResponseYou've already chosen the best response.0Using Maple I've found: trapezoid rule gives 2.432066146 Simpson's rule gives 2.430797145

unimatix
 one year ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{a}^{b}\frac{ x^2 }{ \sqrt{(1x^2)(k^2x^2)} }\] a = 3 b = 5 k = 2

unimatix
 one year ago
Best ResponseYou've already chosen the best response.0@SolomonZelman @pooja195

unimatix
 one year ago
Best ResponseYou've already chosen the best response.0Even if someone just has an idea that might be helpful.

dan815
 one year ago
Best ResponseYou've already chosen the best response.2error bound on simpsons rule

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0you want to confirm this numerically or you want to prove it using the error bound theorem

dan815
 one year ago
Best ResponseYou've already chosen the best response.2i think to find error bounds for trapezoidal one

dan815
 one year ago
Best ResponseYou've already chosen the best response.2take all right end points and all left end points

dan815
 one year ago
Best ResponseYou've already chosen the best response.2the true value is between those 2 answers

dan815
 one year ago
Best ResponseYou've already chosen the best response.2if 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
 one year ago
Best ResponseYou've already chosen the best response.0Okay thanks I'll try and see if I can figure out how to do that.

dan815
 one year ago
Best ResponseYou've already chosen the best response.2I am not completely sure about this argument though

dan815
 one year ago
Best ResponseYou've already chosen the best response.2it 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
 one year ago
Best ResponseYou've already chosen the best response.2yeah throw that method out of the window, there is a more mathematical way

dan815
 one year ago
Best ResponseYou've already chosen the best response.2https://www.youtube.com/watch?v=qVXIU6mKank This tells you about simpsons error bound

unimatix
 one year ago
Best ResponseYou've already chosen the best response.0Hah that's funny I just found that. I don't see one for the Trapezoid rule though :/

dan815
 one year ago
Best ResponseYou've already chosen the best response.2isnt simpsons just a higher order trap

unimatix
 one year ago
Best ResponseYou've already chosen the best response.0I don't really know what that means.

dan815
 one year ago
Best ResponseYou've already chosen the best response.2simpsons rule is just like beight a bit smarter about the trapezoidal rule

dan815
 one year ago
Best ResponseYou've already chosen the best response.2it will take the average of the areas of the trapezoids in a smarter way

unimatix
 one year ago
Best ResponseYou've already chosen the best response.0Okay. So it will be found in a similar way?

dan815
 one year ago
Best ResponseYou've already chosen the best response.2yeah u should understand the pictures of these operations that will make it a lot clearer

dan815
 one year ago
Best ResponseYou've already chosen the best response.2basically for trapezoidal

dan815
 one year ago
Best ResponseYou've already chosen the best response.2we went from line connections to parabollic connections

dan815
 one year ago
Best ResponseYou've already chosen the best response.2u can keep going on in this way

dan815
 one year ago
Best ResponseYou've already chosen the best response.2like higher order simpsons rule, instead of parabola u can do x^3 , x^4,x^5 curve connections

unimatix
 one year ago
Best ResponseYou've already chosen the best response.0Okay that makes sense
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