Calculus Problems & Solutions: Limits to Integrals & Beyond

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daniel_i_l
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Does anyone know were I can find calculus problems with solutions (or answers) from limits to integrals and beyond.
 
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I'm guessing you mean "on the net"?
 
yes - I meant on the web
 
I wouldn't mind finding such a gem myself.
 
So it's gems you want:

You can calculate single integrals (live) online using the mathematica engine via the so-called "The Integrator" found at

http://www.integrals.com

There's a whole host of such things at

http://www.martindalecenter.com/Calculators2.html

There's an interactive java version of Interactive Real Analysis at

http://web01.shu.edu/projects/reals/index.html

"Multivariable Calculus on the Net" at

http://omega.albany.edu:8008/calc3/links.html

some Online Math Quizes (ala Multiple Choice Java Applet) at

http://www.math.ucla.edu/~tao/java/MultipleChoice/MultipleChoice.html

some Online Mathematics Textbooks at

http://www.math.gatech.edu/~cain/textbooks/onlinebooks.html

Distributed Digital Library of Mathematical Monographs Collection hosted by Cornell University is at

http://mathbooks.library.cornell.edu:8085/Dienst/UIMATH/1.0/GenHome

You can fin "Virtual Laboratories in Probability and Statistics" at

http://www.math.uah.edu/stat/

Let us not forget

http://www.equationsheet.com/

the On-Line Encyclopedia of Integer Sequences

http://www.research.att.com/~njas/sequences/Seis.html

Physics and Mathematics for Young Learners

http://kr.cs.ait.ac.th/~radok/math/mat/intro.htm

The usuals, namely

http://mathworld.wolfram.com/

http://functions.wolfram.com/

http://planetmath.org

And, well, that's about enough.
 
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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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