Integration (mathematical) - a bit of help needed

[Daye.04]

Allright. So I have this mathematical problem right here that I'm not able to solve. Don't look at me that way, I'm an electrician, we don't usually integrate =P

Now the function I need to integrate goes as following

F(x)=x(25-x)3

I don't know whether or not this is supposed to be easy or not. i'm at technical college, and our math isn't exactly astro physics. So if it's really simple, that's great! Then everyone is able to help me =D
And if not. Well, then I'm still certain there are a few on here that's still able to help me. Since. Well. Let's face it, Escaperinos are both awesome and smart =D

See, I've like looked just about everywhere, and kind find a solution or any rule that would help me integrate that damn function. So any help is greatly appreciated. Thanks a bunch beforehand, guys =D

Oh, and if you're able to solve it and require a reward ...
I can make you have tentacles instead of legs, just like in this picture ^^
<spoiler=Picture><img=http://www.facebook.com/photo.php?pid=463869&l=d52d58438b&id=100001437556532>

Fine, you got me. It's just that I just realized how to make those tentacles, and it looks frikkin' awesome! =D

 

[Dags90]

It's a pretty tricky integral, not an easy u-substitution problem. Not the kind of problem I want to do out by hand...so...

Wolfram Alpha had this to say. [http://integrals.wolfram.com/index.jsp?expr=x%2825-x%29^3&random=false] Seems reasonable (correct degree), don't forget your constant of integration.

Edit: It's not that tricky if you expand the polynomial, jumped the gun on the complexity of the problem.

 

[Daye.04]

Well, that seems fair enough and all, but I have some problems understanding how Wolfram got there ...

 

[martin's a madman]

Nope, only in grade 12 calculus right now, I can differentiate things, but I can't put them back yet.

I'll give you help when university starts in September : D

 

[Dags90]

Well, that seems fair enough and all, but I have some problems understanding how Wolfram got there ...

It looks like you expand the polynomial and multiply the result by x. Then you integrate each term.

 

[SckizoBoy]

Only thing I can think of is expansion and individual function integration. Therefore:

x(25-x)[sup]3[/sup] = 15625x - 1875x[sup]2[/sup] + 75x[sup]3[/sup] - x[sup]4[/sup]

Integrated: (15625/2)x[sup]2[/sup] - 625x[sup]3[/sup] + (75/4)x[sup]4[/sup] - (1/5)x[sup]5[/sup] + c

*shrug* I'm sure there's an easier way to go about it.

Teehee... haven't done this type of maths in... well, years! ¬_¬

EDITed for shit mental arithmetic.

 

[Melon Hunter]

Multiply it out.
x*(25-x)(25-x)(25-x)
= x*(25-x)(625-50x+x^2)
= x*(15625-1250x+25x^2-625x+50x^2-x^3)
=(15625-1875x+75x^2-x^3)*x
=15625x-1875x^2+75x^3-x^4

Integral should be 7812.5x^2-625x^3+18.74x^4-0.2x^5+c

 

[BoredDragon]

you use u substitution

Spoiler: this is my explanation

u= 25-x
x=25-u

so then the function becomes (25-u)*u^3

from there you distribute the u^3 ---> 25u^3-u^4 and integrate

you will get (25/4)*u^4 - (1/5)*u^5

you then replace u with 25-x to get the real answer

(25/4)*(25-x)^4 - (1/5)*(25-x)^5

I'm a computer science major so I have to know how to do these things

edit:

or you could do the simpler way that everyone else is talking about. Why do I always over-complicate things!?!

*face-desk*

 

[Durananrananrananran]

edit - deleted entire post in shame. listen to the compsci major

 

[Daye.04]

It looks like you expand the polynomial and multiply the result by x. Then you integrate each term.

Oh, yes! Of course, it's obvious. That's what needs to be done. =D
*Goes to look up polynomial*
Thanks for the help, though =D

The ironic thing is, I might already know how to extract this polynomial .. Thing. I only know what everything action is called in Norwegian =P

Edit:
See, I did know how to plolynominal the extract ... Or whatever ^^
Thanks a bunch, guys!

As always, you're the best =D

 

[SckizoBoy]

math snip

Nope, technically, this is the 'easier' way.

*facepalm*

 

[Dags90]

Nope, technically, this is the 'easier' way.

*facepalm*

I was taught to only use u-substitution when there's a function and its derivative present. Pedagogy fail?

Pretty sure the internet is the easiest way though.

 

[MutetheDrunk]

1. Expand the polynomials: (25-X)^3 => (25-X)*(25-X)*(25-X) => (625+X^2-50X)*(25-X) => (15625+25X^2-1250X)+(-625X-X^3+50X^2) => (Simplify) -X^3+75X^2-1875X+15625

So Far: X(-X^3+75X^2-1875X+15625)

2. Factor in X: -X^4+75X^3-1875X^2+15625X

3. Now intergrate: Int(-X^4+75X^3-1875X^2+15625X)dX => -X^5/5+75X^4/4-1875X^3/3+15625X^2/2+C

I don't usually do maths on the internet so make sure to check my work for mistakes

 

[Silent observer]

Edit: In the time it took me to type out my answer, a dozen people have done it much more clearly. Feel free to ignore this post

 

[Daye.04]

Hey, how awesome wouldn't it had been if I were actually in the middle of a math-test now, and you all were basicly doing the test for me ^^

 

[Knusper]

Multiply it out.
x*(25-x)(25-x)(25-x)
= x*(25-x)(625-50x+x^2)
= x*(15625-1250x+25x^2-625x+50x^2-x^3)
=(15625-1875x+75x^2-x^3)*x
=15625x-1875x^2+75x^3-x^4

Integral should be 7812.5x^2-625x^3+18.74x^4-0.2x^5+c

I don't quite agree with the method. I just commissioned my maths-genius friend to figure it out and he said to binomially expand instead of multiplying out. I'll have the answer in a jiffy.

 

[SckizoBoy]

Nope, technically, this is the 'easier' way.

*facepalm*

I was taught to only use u-substitution when there's a function and its derivative present. Pedagogy fail?

Pretty sure the internet is the easiest way though.

Yep, internet is the master of all... well, all.

And no, the 'u' substitution can be used in any context, and here it's a little more convenient to use to prevent the function from being too long. Granted, it wasn't that long when fully expanded, but worth it when you have 4+ polynomial exponentials. The scribbling can get a bit fiddly.

*shrug* Same answer either way, so hey, it works anyway.

 

[Melon Hunter]

Multiply it out.
x*(25-x)(25-x)(25-x)
= x*(25-x)(625-50x+x^2)
= x*(15625-1250x+25x^2-625x+50x^2-x^3)
=(15625-1875x+75x^2-x^3)*x
=15625x-1875x^2+75x^3-x^4

Integral should be 7812.5x^2-625x^3+18.74x^4-0.2x^5+c

I don't quite agree with the method. I just commissioned my maths-genius friend to figure it out and he said to binomially expand instead of multiplying out. I'll have the answer in a jiffy.

It's the most intuitive method, that's all. Definitely not the fastest, but I think it's easier to follow the thread of logic this way.

 

[Knusper]

Multiply it out.
x*(25-x)(25-x)(25-x)
= x*(25-x)(625-50x+x^2)
= x*(15625-1250x+25x^2-625x+50x^2-x^3)
=(15625-1875x+75x^2-x^3)*x
=15625x-1875x^2+75x^3-x^4

Integral should be 7812.5x^2-625x^3+18.74x^4-0.2x^5+c

I don't quite agree with the method. I just commissioned my maths-genius friend to figure it out and he said to binomially expand instead of multiplying out. I'll have the answer in a jiffy.

It's the most intuitive method, that's all. Definitely not the fastest, but I think it's easier to follow the thread of logic this way.

Yeah I just figured it out and got to where you are so you were right after all, sorry.

It's a pity because I have an exam on this on Monday and I clearly don't know anything about it.

 

[Melon Hunter]

Multiply it out.
x*(25-x)(25-x)(25-x)
= x*(25-x)(625-50x+x^2)
= x*(15625-1250x+25x^2-625x+50x^2-x^3)
=(15625-1875x+75x^2-x^3)*x
=15625x-1875x^2+75x^3-x^4

Integral should be 7812.5x^2-625x^3+18.74x^4-0.2x^5+c

I don't quite agree with the method. I just commissioned my maths-genius friend to figure it out and he said to binomially expand instead of multiplying out. I'll have the answer in a jiffy.

It's the most intuitive method, that's all. Definitely not the fastest, but I think it's easier to follow the thread of logic this way.

Yeah I just figured it out and got to where you are so you were right after all, sorry.

It's a pity because I have an exam on this on Monday and I clearly don't know anything about it.

Hey, no need to apologise! I'm glad you were able to figure it out! Good luck with the exam. Is it just on calculus or is it on a range of topics?