Physical Interpretation of Integration

[Hamza Abbasi]

I always wondered that what is the physical interpretation of integration . How come integrating position gives as velocity? Can some one explain me what is physical insight of integration ? Ignore my poor communication skills.

 

[Dr. Courtney]

Integrating position does not give velocity.

I think of integration as accumulation. A moving object accumulates change in position, so the integral of velocity is the total change in position.

 

[Hamza Abbasi]

Integrating position does not give velocity.

oh sorry for that

 

[Hamza Abbasi]

Integrating position does not give velocity.

I think of integration as accumulation. A moving object accumulates change in position, so the integral of velocity is the total change in position.

Wow ! I never thought this analogy for integration . Can you please further elaborate with giving some more examples.

 

[mathman]

Integral of height (of curve) is area under curve.

 

[Bandersnatch]

Hyperphysics has got a nice tutorial:
http://hyperphysics.phy-astr.gsu.edu/hbase/integ.html#c1

To help with physical visualisation, whenever they use the general term f(x) imagine it's the velocity function V(t).

 

[Drakkith]

Can some one explain me what is physical insight of integration ?

You're best bet is to learn calculus, which is all about integration and differentiation.

Short of that, the answers above are pretty good. But without learning calculus, you're going to understand integration about as well as someone who knows the different colors but never learned to paint or color.

 

[sophiecentaur]

so the integral of velocity is the total change in position.

You would need to integrate over an appropriate quantity. In this case, it would be time ∫v(t) dt = s. Integration (the definite integral) involves two things. It is the reverse of differentiation and it is calculated between limits ( start and end values) The limits are important where Physics is concerned. There is often but not necessarily the idea of an area 'under a graph' involved, which is how the idea is mostly approached when you learn about Calculus.
@Hamsa
You really need to learn about Calculus if you want any deep appreciation of what it's all about. There are some very strict rules involved in what you can do and how to do it. Without knowing the rules, it is just arm waving. The only things you can know about Calculus, without doing it formally, is that differentiation is about the rate at which one quantity changes with another quantity and that definite integration is about summing things up. Maths is definitely worth getting into and constantly advancing with whatever level you are at at the moment.