Calculating Lower Sum for f(x) = x^2 +1 between 0 and 2 with Change in X = 1/2

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Find lower sum...please help!

Homework Statement


Find the lower sum for f(x) = x^2 +1 between 0 and 2 using a change in X = 1/2


Homework Equations





The Attempt at a Solution


[(0^2 + 1) * 1/2] + [(1/2^2 + 1) * 1/2] + [(1^2 + 1) * 1/2] + [(3/2^2 + 1) * 1/2] = 3.75

Is this right?
 
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Seems ok to me.
 
It would be better to use parentheses for things like (3/2)^2= 9/4 (not 3/2^2= 3/4) but, in fact, you've done that exactly right.
 
Thank you! Is there a way to check this on my calculator?
 

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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