Riemann Sum: Solve for Area Under Curve 0 to 18

blahblah33
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Riemann sum help!

Homework Statement


Use Riemann sum with ci= i3/n3
f(x)= \sqrt[3]{x} +12
from x=0 to x=18
n= 6 subintervals
Approximate the sum using Riemann's Sum

Homework Equations


\Sigma f(ci) \Delta xi
is the equation for riemanns sum i think

The Attempt at a Solution


i tried plugging in stuff using that, but i must've done something wrong because the answer i got was 200 off the actual area under the curve...
 
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also, is my original equation for riemann's sum correct? is there a limit involved?
 

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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