Question about error theorem for simpsons rule

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    Error Theorem
badtwistoffate
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it is:
E=|I-Sn|>= (k4 (b-a)^2 )/ (180 n^4)

I know what all of the parameters mean except I, what is it again? It can't be the integral as that's why were using simpsons rule so is it a guess or?:blushing:
 
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It is, in fact, the integral. Just because you don't know what it is doesn't mean you can't write an equation about it. S_n is the "n" guess.

Carl
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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