(OT) Calculus Help for Morons

[Wolf72]

But math is deeply rooted in philosophy and faith, it'd be good from a historical perspective.

I think you're just trying to get me to have a Calculas siezure

 

[kingpaul]

I think you're just trying to get me to have a Calculas siezure

Actually, no. Math is based entirely on faith. What is the most basic mathematical question? What is 1 + 1? 2. Why is this? We take this on faith that it is true. Taking the class filled with the proofs of calculus just goes to show how much we take for granted in the mathematical arena.

 

[orbitalfreak]

1 = 2

I wouldn't too much trust placing faith in mathematics, though. Ask yourself this question: "Is there any possible way that one could equal two?" The answer is, "Of course not!" Or is it...

Let x and y be arbitrary integers such that x = y. Then,

x=y // given
x² = xy // multiply each side by x
x² - y² = xy - y² // subtract y² from each side
(x+y)(x-y) = y(x-y) // factor
x+y = y // divide by (x-y)
2y = y // Substitute, since x = y, as given
2 = 1 // Divide by y.

Mathematical proof that 1 = 2.
Yeah, it's not true, nor is it a properly constructed proof since we used illegal math, but it's still funny.

 

[Sir Whiskers]

Orbitalfreak, it took a bit, but I see now why you say it's illegal:

dividing by (x-y) is the same as dividing by 0 (which is illegal).

Still, I have to send this to a few friends and watch their eyes glaze over.

 

[Sir Whiskers]

Kingpaul, I agree math is based on faith, but not your example. 1+1=2 is true since we have first defined what 1 and 2 mean. Two is always equal to 1+1 because that's part of the definition of "2".

Where I believe math begins to take on elements of faith is our belief that mathematical formulas can represent reality. We can prove formulas to be accurate to our heart's content (within their narrow definitions), but so what? They're only important if they tell us something about the universe, and *that* we take on faith. ("What Mr. Einstein? All this math of yours defines how space-time works? How do you *know* that? Prove it.")

Of course maybe the real benefit is that we can never prove these things 100% - and all the arguing brings us closer to the truth, whatever that is.

Okay, enough metaphysics for one day...

 

[jgbrowning]

Okay, enough metaphysics for one day...

Metaphysics? This is abuse, metaphysics is room 12A, next door.


joe b.

 

[Wolf72]

urk!

*wolf's brain begins to turn to mush ... and he starts hearing Mr. Yuengling's voice in the distance .... " use the asymtote to ... " *

 

[Dinkeldog]

Just remember: regardless of what you get on the AP test, take Calculus in college. This goes especially if you're looking at a technical degree. You're not suffering through a year's worth of classes you could avoid (thereby speeding up graduation by that much--logical fallacy, as graduation is never sped up, only delayed), you're padding your GPA with a year's worth of A's.

 

[Trevalon Moonleirion]

Just remember: regardless of what you get on the AP test, take Calculus in college. This goes especially if you're looking at a technical degree. You're not suffering through a year's worth of classes you could avoid (thereby speeding up graduation by that much--logical fallacy, as graduation is never sped up, only delayed), you're padding your GPA with a year's worth of A's.

Dink... I'm going to be a history major. I want to teach high school history. If I take calculus in college... well damn taht's just masochistic of me!

Look at what a crazy thread I started, all over two stupid homework problems... I love this place!

Thanks for all the help!

 

[Trevalon Moonleirion]

(1)
∫ (sin³x)(cos²x)dx
= ∫ (sinx)(sin²x)(cos²x)dx
= ∫ (sinx)(1-cos²x)(cos²x)dx
= ∫ (sinx)(cos²x - cos⁴x)dx

Let u = cosx
then du = (-sinx)dx

So,
∫ (sinx)(cos²x - cos⁴x)dx
= -∫ u² - u⁴ dx
= - ((1/3)u³ - (1/5)u⁵) +C

clean it up, supstituting back for u, the final answer is

(1/5)cos⁵x - (1/3)cos³x + C
//

(2)

∫₀¹ 1/(√(4-x²)) dx
This is a standard integral of the form
∫₀¹ 1/(√(a²-x²)) dx
= arcsin (x/a) + C

in this case, a² = 4, so a = 2. Substitute this, and you get

arcsin(x/2)¦₀¹
= arcsin(1/2) - arcsin(0/2)
= arcsin(1/2)
= π/6 <-- That's a (pi over six), if it doesn't show up.
//

How'd you get all the nifty math symbols onto the boards? And... these standard integrals... I'm a teensy bit puzzled how they work...?