Is Relying on Integral Tables Over Manual Calculation Common in Physics Careers?

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In summary, as time goes by in the physics career, there is a growing reliance on integral tables and computer programs for solving integrals. This is seen as a more efficient and less tedious method, especially for integrals involving multiple integrations by parts or trigonometric functions. However, there is a concern that this could lead to a lack of understanding and recognition of incorrect answers, particularly for those with little experience with integrals. Some suggest that using programs and tables should be reserved for known integrals, while others enjoy the challenge of solving new and complex integrals. There are also options for free programs, such as Maxima, but it is important not to rely too heavily on computers and to still have a basic understanding of integration
  • #1
dipole
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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?
 
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  • #2
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 into 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.
 
  • #3
I have better things to do than waste time on integrals I've already done before.
 
  • #4
dipole said:
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?

It is still best to do it if that is the first time you see such integrals.
 
  • #5
Tables? I just shove them in Mathematica.
 
  • #6
K^2 said:
Tables? I just shove them in Mathematica.

Is there a free version of Mathematica?

Not a 30-day trial either.
 
  • #7
Neandethal00 said:
Is there a free version of Mathematica?

Not a 30-day trial either.

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.
 
  • #8
Sometimes I've needed a general expression rather than a number, so I've had to solve integrals for that.
 
  • #9
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! :smile:
 
  • #10
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.
 
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  • #11
Neandethal00 said:
Is there a free version of Mathematica?

Not a 30-day trial either.

MMA isn't free but Maxima is.
 
  • #12
Neandethal00 said:
Is there a free version of Mathematica?

Not a 30-day trial either.

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

http://maxima.sourceforge.net/
 
  • #13
  • #14
Neandethal00 said:
Is there a free version of Mathematica?
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.
 
  • #15
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.
 
  • #16
sophiecentaur said:
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.

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.
 
  • #17
sophiecentaur said:
After all, GIGA applies whenever computers are involved. You need to be able to recognise garbage when it comes out.

Wouldn't that be GIGO?
 
  • #18
Yep. I guess that sort of makes my point. Haha.

I guess the "A" could stand for the Essex pronunciation "AAHT"
 
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Related to Is Relying on Integral Tables Over Manual Calculation Common in Physics Careers?

1. What is integration?

Integration is the process of combining different parts or elements into a whole. In science, integration can refer to combining different research findings or approaches to gain a more comprehensive understanding of a topic.

2. How is integration used in scientific research?

Integration is commonly used in scientific research to combine data from multiple sources or disciplines, synthesize findings from various studies, and develop new theories or hypotheses. It can also be used to bridge the gap between different fields and promote interdisciplinary collaboration.

3. Why is integration important in science?

Integration is important in science because it allows for a more holistic and nuanced understanding of complex phenomena. By combining different perspectives and approaches, scientists can gain a more complete picture of a topic and make more accurate conclusions.

4. What are some challenges of integration in science?

One challenge of integration in science is the potential for conflicting or contradictory findings from different sources. This can lead to difficulties in reconciling different perspectives and can require careful analysis and interpretation to reach a coherent understanding.

5. How can scientists effectively integrate their research?

To effectively integrate their research, scientists can use a variety of methods such as meta-analysis, literature reviews, and interdisciplinary collaborations. They can also communicate and collaborate with experts from different fields to gain different perspectives and insights.

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