Do you bother to integrate?

dipole

As time goes by in my physics career I find myself less and less motivated to do integrals by hand and more relying on integral tables to quickly look up the answer. I just find doing integration out by hand tedious, especially ones that require multiple integrations by parts or involve trig functions.

What are your thoughts on integrals?

elfmotat

As long as you understand how you would go about solving the particular integrals, and you're not taking a class where you're graded on your ability to solve them by hand, why waste your time? Just look them up in a table or plug them in to a program.

The only danger with doing this is when people with little experience with integrals don't know what the right answer should look like, so if the computer gives them a wrong answer they won't be able to recognize it. As long as you understand the process and have a general idea of how the answer should look, I don't see the harm in using programs/tables.

Pengwuino

I have better things to do than waste time on integrals I've already done before.

Dr_Scientist

It is still best to do it if that is the first time you see such integrals.

K^2

Tables? I just shove them in Mathematica.

Neandethal00

Is there a free version of Mathematica?

Not a 30-day trial either.

Pengwuino

Wolfram Alpha can do integrals I'm pretty sure. It's just not as easy to type out complex ones. You can probably get mathematica pretty cheap if you attend a university.

DragonPetter

Sometimes I've needed a general expression rather than a number, so I've had to solve integrals for that.

Infinitum

Wolfram Alpha and a few others can do indefinite as well as definite integrals with arbitrary constants. The only trouble is typing the equation out correctly with complex equations...

As for bothering to integrate, I don't if I already know how to integrate the expression, however long it might turn out.

Its always fun to try out new, never-seen-before integrals!

PlanckShift

Try a calculator that does integrals like HP50g or TI89ti. The 50g has an Equation Writer so you see the expression written out in Pretty Type.

PlanckShift

MMA isn't free but Maxima is.

viraltux

Try Maxima, it is a FOSS project and works very well

http://maxima.sourceforge.net/

PlanckShift

Once you get Maxima you can use an editor like TeXmacs.

K^2

A lot of universities have free licenses for their students. That's how I got my license. Otherwise, you have to pay or use an alternative program.

You can, indeed, do a lot of things with Wolfram Alpha, but if your integral times out, you are out of luck. For integrals, you can use Mathematica syntax to make sure Alpha doesn't screw up.

sophiecentaur

Trouble is that there is a risk of relying on the computer too much, to do your thinking for you. It must be good for people to go through the agony of basic integration and learning how to solve differential equations and not to reach for Mathematica before you even have an idea what it is doing for you.
There's a similar problem with this new generation of students and the reliance on circuit simulation programs rather than using analysis methods even for the simplest problems. (And using calculators to multiply by 100!)
I wouldn't be without computers to help me but I couldn't bring myself to rely entirely on what they tell me. After all, GIGA applies whenever computers are involved. You need to be able to recognise garbage when it comes out.

dipole

Yes I agree with this, which is why I prefer not to use Wolfram. At least with a table I may need to manipulate the integral slightly to get it into a desired form, which hopefully will make me more careful. With computers you can be exceptionally lazy.

Nabeshin

Wouldn't that be GIGO?