Double Integration: Approximating R Bounded by y=x2 & y=1

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Homework Statement



How to approximate the \int \inte x2 dA where R is bounded by y=x2 and y=1.
 
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There are any number of ways to approximate a definite integral. What have you tried so far?
 
Mark44 said:
There are any number of ways to approximate a definite integral. What have you tried so far?

I can't start to do,I don't know how to start.
 
If you have never seen a numerical integration, why are you trying to do this problem?

Look up "Simpson's Rule".
 

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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