# Integration-By-Parts Man!

#### FortKnox (169099) writes | more than 9 years ago

21
Heh, my old roommate used to refer to me as "Integration-by-parts man" because I was really good at integration by parts. Last time I used integration by parts was calc III (maybe calc II). I don't think I ever needed complex enough integration in any of my core classes to require integration by parts.Heh, my old roommate used to refer to me as "Integration-by-parts man" because I was really good at integration by parts. Last time I used integration by parts was calc III (maybe calc II). I don't think I ever needed complex enough integration in any of my core classes to require integration by parts.

One of my family friends is in college (my school, my degree with some influence by me) who is having trouble with it. Seeing that I took calc3 in the beginning of 1996, I'm a little nervous about teaching (let alone seeing if I remember it well enough to work the problems myself). I don't have my calc book anymore, so it looks like I'll have to peruse the web to a page that has a little explanation to jog the 'ol noggin and maybe some problems I can work through. I don't suppose anyone knows a site like that (I really do not want to pay $100 for a calc book, if at all necessary).

## It came back to me surprisingly well (1)

## johndiii (229824) | more than 9 years ago | (#8260763)

## Last time I did it... (1)

## Some Woman (250267) | more than 9 years ago | (#8260782)

And No. I don't know of any resources. Might try going to Barnes and Noble- they might have a tutorial that you can peruse in the store.

## Re:Last time I did it... (1)

## FortKnox (169099) | more than 9 years ago | (#8260836)

## Re:Last time I did it... (2, Funny)

## robi2106 (464558) | more than 9 years ago | (#8262324)

You've never seen Calculus like this before!

Un cut and uncensored!

Buy now and we will throw in, absolutely free...

Calculus Spring Break!

jason

## I actually used it once... (1)

## dmorin (25609) | more than 9 years ago | (#8260815)

I got to use it once, about a year out of college, when I worked for a digital signal processing group and we wanted to check something manually to see if it was approx. the expected result.

## just remember ... (1)

## Abm0raz (668337) | more than 9 years ago | (#8260880)

-Ab

## Re:just remember ... (1)

## FortKnox (169099) | more than 9 years ago | (#8261125)

## Book price (1)

## Tet (2721) | more than 9 years ago | (#8261527)

I really do not want to pay $100 for a calc book, if at all necessarySo don't. I know that text books are expensive in the US, but they don't have to be that expensive. Anyway, the book you're looking for is "Engineering Mathematics" (or possibly "Advanced Engineering Mathematics", check the contents of both), by K.A. Stroud. Amazon US have it for US$60. It's cheaper from Amazon UK, although check the shipping price (I can ship it for you if necessary).

## I think I speak (1)

## blinder (153117) | more than 9 years ago | (#8261592)

Huuuuhhhh?????

## Re:I think I speak (1)

## robi2106 (464558) | more than 9 years ago | (#8262251)

Calc III unlike the previous two classes, was kind of fun. I mean... You get to deal with vectors, and fun visual stuff and math in 3D.

jason

## Re:I think I speak (1)

## mekkab (133181) | more than 9 years ago | (#8262635)

Hooray for the cross product! Hooray for the Del operator! Hooray for Maxwell!

## Re:I think I speak (1)

## robi2106 (464558) | more than 10 years ago | (#8270531)

But I switched to computers to avoid the evil Organic chemistry class. Well that and I kept getting summer jobs in computers instead of chemistry so I eventually took the hint.

jason

## Re:I think I speak (1)

## mekkab (133181) | more than 9 years ago | (#8262699)

Calculus is the mathematics of change. Just remember that you too, are a vector. Now get your vector ass back to work or I'll integrate

youby parts!## Re:I think I speak (1)

## blinder (153117) | more than 10 years ago | (#8269175)

Just keep nodding and welcoming your Calculating overlordsits what i *do*!

Now get your vector ass back to work or I'll integrate you by parts! ;)damn you mekkaman!!!

in Mekka's Russia parts integrate you!

## Beautiful Integrals (1)

## Morosoph (693565) | more than 9 years ago | (#8262925)

How to find it is sheer beauty...

Let I=Integral {e^-(x^2)}dx, then I^2=[Integral {e^-(x^2)}dx]*[Integral {e^-(y^2)}dy]

Since x and y are independent variables, I^2=Integral Integral {{[e^-(x^2)]*[e^-(y^2)]}}dxdy

so I^2=Integral Integral {{e^-[(x^2)+(y^2)]}}dxdy

I hope that my fellow mathematicians will allow me to skate over the rigour here (as I'm a little^H^H^H^H^H^H^H^Hvery rusty) whilst I invoke geometrical intuition with a flourish of hand-waving:...

We're integrating over the plane to get I^2, so let us see what happens when we switch variables to r and t (for theta). As we sweep around the radius of a concentric circle, we find that the distance swept around is rdt in angle dt, so that (unrigourous bit) we can replace dxdy with rdrdt as a result of changing variables. Notice also that x^2+y^2=r^2 (Pythagoras), so that our integral becomes:

I^2=Integral Integral {{r*e^-(r^2)}}drdt=[Integral {1}dt]*[Integral {r*e^-(r^2)}dr]

so I^2=2Pi*Integral {r*e^-(r^2)}dr (evaluated between r=0 and r=+inf)

But d(e^-(r^2))/dr=-2re^-(r^2), so that our integral becomes:

I^2=-Pi*[e^-(r^2)] (between r=0 and r=+inf)

so I^2=-Pi((e^-inf) - (e^0))=-Pi(0-1)=Pi

ie. Our original integral I=Integral {e^-(x^2)}dx evaluates to sqrt(Pi). Beautiful!

## Calculus? I did that at A-levels (Sixth Form) (1)

## MonTemplar (174120) | more than 9 years ago | (#8263099)

Ditto for Statistic. Know the principles, buggered if I can remember how to apply it.

But Logic? Yeah, I know Logic? Every which way. God help me!

-MT.

## pulls out old 220 notes, digs through and finds (2, Informative)

## http (589131) | more than 10 years ago | (#8264612)

in particular...

http://www-math.mit.edu/~djk/18_01/chapter24/cont

pain beginning behind left eye...

## google is your friend (1)

## TechnoLust (528463) | more than 10 years ago | (#8266082)

## Integration by Pants (1)

## andfarm (534655) | more than 10 years ago | (#8266492)

## Check out ebay and half.com for used books.... (1)

## (H)elix1 (231155) | more than 10 years ago | (#8266730)

Just for the record, power series still suck...

## Psst...free book (1)

## Pinball Wizard (161942) | more than 10 years ago | (#8337396)

Email me an addy and I'll get it out to you.