Question

When do you exactly use the integral symbol in an equation?? equations like the faraday's law or gauss's law always confuses the heck out of me! @_@

Answer 1

Have you a calculus-based physics textbook? Or just a calculus textbook? Either one would give you concrete examples of where integration is necessary to obtain some quantity.

For example (if I remember correctly), the voltage across an inductance (electrical component) is a multiple of \[\int\limits_{}^{}i dt\]

Answer 2

No sadly, I don't. :(

Answer 3

I'd rather that you learn where to use the integral symbol in particular situations such as this one.

If you have a graph such as y=x^2 + 2, the AREA UNDER THE GRAPH AND ABOVE THE X-AXIS, on the interval [a , b], is \[A = \int\limits_{a}^{b}f(x) dx\]

Answer 4

Oooooooh I see!! that's interesting!
I always wondered what they were!

Answer 5

haha

Answer 6

I did a search for "applications of definite integrals" and came up with quite a number of hits:

https://www.google.com/search?q=applications+of+definite+integrals&rlz=1C1CHFX_enUS461US461&oq=applications+of+definite+integrals&aqs=chrome..69i57j0l5.5080j0j7&sourceid=chrome&espv=210&es_sm=122&ie=UTF-8

If you'd please look thru a few of these, it's practically guaranteed that you'll find examples of applications of definite integrals.

Glad you find this to be "interesting!"

Answer 7

good luck. Come back with specific integrals, definite or indefinite, and we'll work on them.

Answer 8

thank you! :D

Answer 9

In a slightly more general sense, an integral essentially means that you're adding a bunch of things up. In Gauss' Law, for example, you're adding up the "amount" of electric field that passes through a particular surface, while in Faraday's law, you're adding up the "amount" of electric field you have to fight through while walking in a loop.

Both of those descriptions are WILDLY qualitative, and to understand them on a deep level you'd need to understand much more math - but that's the idea. Integral -> Adding stuff up.

Answer 10

Awwwww I'm not taking maths at the moment :(

Answer 11

but wait you said "electric field you have to fight through while walking in a loop"
what do you mean by that?

Answer 12

Again - if you don't understand the physics or the math, any explanation I give is going to sound confusing, I'm afraid.

Answer 13

Example - what I really mean is that in Faraday's law, you calculate the line integral of the electric field around a closed loop. At each step, you see some electric field - you calculate its projection along your direction of motion, add that to your total, and continue going until you've completed your loop. But as I'm sure that makes very, very little sense, it's not worth thinking about without doing it properly.

Answer 14

I got it now haha I may not be taking maths as one of my subjects but I'm certainly taking physics so I understood it almost until I saw the word loop and I got confused thinking what loop your talking about.

Answer 15

They are very intimately tied together - not understanding calculus means that you cannot possibly understand physics, at least not really - it's good that you are getting a feel for the material in the meantime, though, and once you learn more math it will become much more clear and wonderful.

Answer 16

You are right! physics will go no where with an equation to prove! Hahaha!!! xD

Answer 17

*without