Need Help with Calculus? Check out this Comprehensive Study Guide for Area!

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I was wondering if anyone might know of an online study guide for area? Where it starts off with anti-differentiation and goes through sigma notation, riemann sums, indefinte integral, to Fundamental Theorems of Calculus and Definite Integrals. It would be a gem and a life-saver. Thanks!
 
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When I first started selfstudying for Calc, I used this site. It has modules, problem sets, explanations, tutorials for Calc I and II.

http://archives.math.utk.edu/visual.calculus/4/index.html

That section there should cover everything you desire and more for integration.
 
That is one nice page! Thanks!
 

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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