Direct integration by substitution

GeoMike
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Definite integration by substitution

I just need a check on this, the book and I are getting different answers...

The problem and my answer:
http://www.mcschell.com/p14.gif

http://www.mcschell.com/p14_worked.jpg

The book gives 0.00448438 though. :confused:

Thanks!
-GeoMike-
 
Last edited by a moderator:
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Your answer looks right. Maybe you copied the question wrong?
 
Your answer is correct, assuming that you gave us the correct problem.

Nice work, by the way - very neat handwriting!
 
I'm sure they mistyped the answer in the book.

Daniel.
 
Last edited:

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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