Hard math problem

[Nat Turner]

I had to do this for part of a physics problem, until I saw the hint that provided the answer to this nearly impossible integral. I want to see if anyone can actually do it.

Integrate dx/[ (a^2+x^2)^(3/2) ].

First one to do it wins a prize!

 

[rosseh]

The answer is 42.

 

[Naudian]

I agree.

/does not know this math

 

[LiquidToast]

I give up, I hate physics >.< I'll stick with chem.

 

[dream431ca]

I used to do intergration..but forgot how...and I don't feel like digging up my notes to remember.

 

[kirovman]

I used to do intergration..but forgot how...and I don't feel like digging up my notes to remember.

Same, used to do some really heavy integration, but now it's mostly gone. I guess it'd come back to me pretty quick if required.

 

[Dekstar]

I've just done integration and I don't even understand that

 

[dream431ca]

Ok fine...I did it...but you didn't tell us if it was respect to a or x so I did both of them and they both turned out the same. And squarer means there is a square root and endsquarer is where the square root ends for that particular function.

Respect to X and A =

3/8 log(x+squarer[a^2+x^2]endsquarer a^4+squarer[a^2+x^2]endsquarer [(x^3/4+5a^2x/8))]

If you would like, I'll do it in word and copy and paste it here so it's easier to understand.

 

[Nat Turner]

Ok fine...I did it...but you didn't tell us if it was respect to a or x so I did both of them and they both turned out the same. And squarer means there is a square root and endsquarer is where the square root ends for that particular function.

Respect to X and A =

3/8 log(x+squarer[a^2+x^2]endsquarer a^4+squarer[a^2+x^2]endsquarer [(x^3/4+5a^2x/8)]

If you would like, I'll do it in word and copy and paste it here so it's easier to understand.

I'm gonna check that in the calculator, but I'm pretty sure it's wrong (at least not the answer they give). It reduces to something much simpler by the way.

And yeah it's respect to x, that's why it put dx over it.

edit:

Is that whole thing inside the first log? you don't have a closing ')'

 

[dream431ca]

I'm gonna check that in the calculator, but I'm pretty sure it's wrong (at least not the answer they give). It reduces to something much simpler by the way.

And yeah it's respect to x, that's why it put dx over it.

Well integration and simplification are 2 different things..you never told me to simplify it just integrate it..that's what I did.

EDIT: the whole thing is logged.

 

[Nat Turner]

Well integration and simplification are 2 different things..you never told me to simplify it just integrate it..that's what I did.

Is the whole thing inside the log tho (you don't have a closing ')' )? And is it log based 10 or natural log? I'm gonna see if it checks out in the calculator.

 

[dream431ca]

Is the whole thing inside the log tho (you don't have a closing ')' )? And is it log based 10 or natural log? I'm gonna see if it checks out in the calculator.

Well of course it's based 10. and yes the whole thing is inside the log. Fixed my bracket mistake.

 

[Ikerous]

http://www.calc101.com/webMathematica/integrals.jsp#topdoit

 

[Nat Turner]

Well of course it's based 10. and yes the whole thing is inside the log. Fixed my bracket mistake.

It doesn't check out on my graphing calculator. The integral of dx/[ (a^2+x^2)^(3/2) ] from x=0 to x=1 where a=1 is ~.7071. The solution for the integral that the hint gave me is also ~.7071 when I plug in x=1 and a=1 (so their answer is right).

When I plug x=1 and a=1 into your equation, I get ~.2109, so it's wrong unless I typed it in incorrectly. Try it yourself if you don't believe me.

 

[Dan]

x(a^2+x^2)^2/a^2

 

[dream431ca]

It doesn't check out on my graphing calculator. The integral of dx/[ (a^2+x^2)^(3/2) ] from x=0 to x=1 where a=1 is ~.7071. The solution for the integral that the hint gave me is also ~.7071 when I plug in x=1 and a=1 (so their answer is right).

When I plug x=1 and a=1 into your equation, I get ~.2109

Well I tried to simplify it...and it comes out to a little longer expression. So either I'm doing something wrong or the equation cannot be simplified.

 

[Ikerous]

a^(-3)*x*(1+(x/a)^2)^(-1/2)

 

[Nat Turner]

a^(-3)*x*(1+(x/a)^2)^(-1/2)

Ikerous wins!!!

It's always equal to the answer the problem gives.

edit:

better picture

 

[dream431ca]

Ikerous wins!!!

It's always equal to the answer the problem gives.

BOO!! Oh well.

 

[Lou]

Ikerous wins!!!

It's always equal to the answer the problem gives.

edit:

better picture

yee I am such an idiot. I took Calculus AP 5 years ago, got a 5, and now I am clueless. Oh well....

 

[Jack_Karverboy]

56a/427(23^6x5)

I just put random stuff. Am I right.

 

[Dan]

never mind, I had that answer but I wrote it down wrong

 

[Nat Turner]

56a/427(23^6x5)

I just put random stuff. Am I right.

lol no.. that would give a wicked tiny decimal. I don't even have to put it into the calculator.

 

[Nat Turner]

This is the original problem by the way, the hardest part is doing the integral (if you don't look at the hints).

 

[Danimal]

The answer is still 42. Bitches.

 

[Nat Turner]

The answer is still 42. Bitches.

But 'X' needs to be in the answer!! lol

 

[Lou]

But 'X' needs to be in the answer!! lol

is that physics 101?

 

[kirovman]

ah, I remember doing that kind of thing in physics.

But now I'm more involved in Scalar waves :O