Laplace Transform (correct, or not?)

noobish
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I wish someone would help me to verify my answer and working. I don't have the answer for the question. :frown:

http://www.mrnerdy.com/forum_img/laplace.jpg


Is there a better working method?
 
Last edited by a moderator:
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My browser shows that your image is broken. Can you either post it as an attachment or type it up in LaTeX?
 
im sorry. I've fixed it. :)
 
Hello Tom,

the image shows up in my browser, so I'll attach it in this post.

Regards,

nazzard
 

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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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