sin(60) (assuming degrees) is [unparseable or potentially dangerous latex formula]. Square this to get 3/4, multiply by 8 to get 6.
[unparseable or potentially dangerous latex formula]. Expand the denominators to where you get products of numbers that are n distance away on the number line and 'chain', as you can see. Put the number of terms over the first in the expansion of the denominators times the last. Hopefully you get that pattern.
This is an approximation. [unparseable or potentially dangerous latex formula], so [unparseable or potentially dangerous latex formula].
[unparseable or potentially dangerous latex formula].
polar to rectangular means: [unparseable or potentially dangerous latex formula]. plugging in r and [unparseable or potentially dangerous latex formula], you get 1.5. Learn polar coordinates and how to convert between polars and rectangulars.
212 x 202 = 424 x 101 = 42824.
142.857 x 63 ~ 1000 / 7 x 63 = 9000
umm... integrals take a long time to explain. I really don't know how long it would take to include the full lesson + the LaTeX + the proofread, and whatever else, so maybe this will help you:
http://en.wikipedia.org/wiki/Integral. There are lots of things you don't need to know that are in there, but basically, learn how to antidifferentiate polynomials, trig, and logs/exponentials, then learn the fundamental theorem of calculus where it says F(b) - F(a) somewhere in there.