Can you check my work? power series representation

Jac8897
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can you check my work? "power series representation"

is ok I figure it out.
 
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Jac8897 said:

Homework Statement




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http://img94.imageshack.us/img94/841...ter5page15.jpg

is my process and answer right?

thanks
jac8897


Homework Equations





The Attempt at a Solution


URL Is bad...
 
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NastyAccident said:
URL Is bad...

ok the url is fix
 


bump:smile:
 

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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