Tip: When determining a time limit, remember that players won't be as familiar with the level as you are. If you normally complete the level with the timer around 100, others might run out of time on their first try.
So for those who find pi * r^2 too hard, you've devised a formula that requires you to calculate the circumference? In my experience, most problems just give you the radius and makes you use that for most things - any backwards calculation is simple enough to do on your own.
Ruby, you make me feel so junior. I can barely understand what you mean
Then clearly you have not taken Geometry or Algebra II.
About the proof you did there, that equation is not used for a reason. Like Incognito said, 1/2tau r^2 is used because it is much simpler and it also does not require as much calculations to derive as yours.
-------------------- Me: Look, matey... it's pronounced ARK-EE-YUS. Got that?
Dude: Ok, you make Arse-ee-yus sound dumb when you say it that way.
Major Flare SMW ASM Moderator, Tools Moderator, and SM64 Manager Torpedo Ted
2 integral signs? All the problems I've faced only used just one! Tho they were for Cartesian coordinates.
A later chapter in my math book has problems with three integral signs.
Simple, Sokoban: You have been studied simple one-dimensional integrals. I presented you some two-dimensional ones. The concept of Riemann's sums applies here too, but now is the sum of volumes, not areas. And the polar coordinates are a different manner of seeing our normal coordinates. This is to make integration over circles easier. And three integrals... they are triple integrals. The form of seeing them as Riemann's sums can be more abstract (some 4-D stuff). And we have other systems of coordinates for them (cylindrical, spherical).
And, finally, the line integrals (and surface integrals). They are more complicated to explain, but they are EXTREMELY important for you to understand some theorems at physics (like the Work, for example - Work can be defined as a line integral).
Because 'pi' is an exact value.
Are surface integrals surface area?
At some point, yes. A surface integral is an area, indeed. But the double integral is a volume, at first, but you can use it to calculate areas, too. You can use even line integrals to calculate some areas. Example: The Si(x) function is an area function, but you use a complex line integral to calculate it, because Si(x) is the integral of sin(x)/x, which doesn't have a primitive.