Solving Riemann Sums for \int_0^{2\pi} x^{2}sin(x)\,dx | Homework Help

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Homework Statement



Express the integral as a limit of Riemann sums. Do not evaluate the limit.

Homework Equations



\int_0^{2\pi} x^{2}sin(x)\,dx

The Attempt at a Solution



I really don't know where to start...any help getting me started would be highly appreciated!
 
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haha i saw that coming before I clicked the url.
 
but seriously just expressing any integral is probably much simpler than you are thinking, all you have to do is basically write down the definition of a Riemann sum here is a better link:

(first equation on page, just substitute your function in)
http://math.fullerton.edu/mathews/n2003/RiemannSumMod.html
 
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alright, seems like I was just over thinking. Thats what I figured. Thanks.
 
happy to help, good luck :smile:
 
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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