<p>The way your "voice" says grass in my mind makes it sound like it has a mystical aura around it...</p>
<p>Phil- I'm in AB and we're doing the same thing this week!</p>
<p>lol
grass is mythical...ahh
princeton = heaven
grass, air, beautiful buildings and oh so safe.
<em>sighsigh</em></p>
<p>Haha, score! Okay, so I'm not in the idiot school. Is it all coming around well for you?</p>
<p>Calculus is gross.</p>
<p>Where is Calculusboy? I want him to dazzle me with his brilliance on my integration problem. It was a homework problem for our class a few weeks ago. I can proudly say that I was the only one who got it. I took BC last year, and we're in the middle of multivariable calc (we finished triple integrals with volumes and are now moving on to surface areas).</p>
<p>Give it to me ForeverZero <em>cracks knuckles</em></p>
<p>I already posted it before, but here it is again:
definite integral of e^(-x^2) dx from 0 to infinity.
I first saw and thought it was impossible. It's tricky, but doable.</p>
<p>yea see i did take AB last year my school doesnt offer BC so im chillaxing for now while i wait to start studying or something for BC... i give myself maybe 1 month before the AP to learn it all... that said, the only reason i find im proficient at math is cuz its the byproduct of having an interest in science...</p>
<p>I envy those of you who can take a solid whack at calculus. Me? I prefer to detail the motivations behind the use of metaphors and other figurative language and how they're used to further the author's attempt to connect his/her reader with an idea. Or better yet, to follow the cyclical natures of the political, legal, and economic processes, determining the facts that influence the exchange and unequal distribution of power. Ah, how I love humanities (except economics isn't technically humanities, but I digress...).</p>
<p>approximation is .886227... I am probably wrong though</p>
<p>Wow... at least you got a handle on it. I saw it and gave up.</p>
<p>Legendofmax, you are correct. The exact answer is actually (root pi)/2.
Basically, you can substitute any variable for x (the same function is going to be performed on it). Let's substitute in y.</p>
<p>If we say that some value n=integral e^(-x^2)dx from 0 to infinity, then
n^2=double integral e^-(x^2+y^2) dxdy from 0 to infinity.</p>
<p>You can then do a polar substitution, in which r^2= x^2 + y^2, and dx<em>dy= r</em>dr<em>d(theta). Remember that an areal unit is dx</em>dy in Cartesian coordinates, and r<em>dr</em>d(theta) in polar coordinates.</p>
<p>So doing this, n^2=double integral e^(-r^2) r<em>dr</em>d(theta).
r is bounded from 0 to infinity, and theta is bounded from 0 to pi/2 (first quadrant).</p>
<p>You can easily integrate theta first, so it becomes n^2= (pi/2) * integral e^(-r^2) r*dr from 0 to infinity. The r integral becomes -e^(-r^2)/2 from 0 to infinity, which is 1/2. Multiply this by the theta integral, so n^2=pi/4. Take the square root of both sides, and n=root pi/2. Ta-da!</p>
<p>Yeah I had trouble with that blasted "r" integral you defined... blahhhh i dunno why. shoulda left it in initial format but hey, I'm happy lol</p>
<p><em>gives you all cotton candy</em>
<em>giggles</em>
<em>bounces off</em></p>
<p><em>chompchomp</em></p>
<p><em>skips off together to noncalculus land of happiness</em></p>
<p><em>Calc God</em></p>
<p>lol but you said it was gross!</p>
<p>I'm the God of gross things then</p>