## purpose of integration/differentiation??

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### purpose of integration/differentiation??

I know how to do integration and differentiation.

But my problem is: why do we need it?
Why do we need to find area under the curve?
What are the real world applications?

There are some examples here -> http://www.intmath.com/Integration/Integration-intro.php but they don't really explain much..

In class we were never told why we need the area under the curve; what it is used for etc.
Cannot find an answer in google and the problem is starting to drive me crazy!!
cka
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### Re: purpose of integration/differentiation??

all these stuff are used in higher education
I'm going to study biomedical science, and all over our course, there are examples of how we would use calculus to help us with the research, although I need to say that we only use Data analysis but. (integration and differentiation are both a part of data analysis)

but as I was in high school myself, it's sometimes hard to concentrate on the problem when you never know what it's actually used for, so you could look at what you want to do in the future, and then look to see where these things are implemented
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### Re: purpose of integration/differentiation??

Though it's more indirect (and cheeky), I would ask in what fields you don't use calculus. Practical psychology?
All but the most elementary forms of measurement use calculus.
All physical sciences use calculus.
Calculus teachers use calculus!

Of course, someone who does math for the beauty (and not necessarily the application) might not be the best to answer this question

The Chaz
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### Re: purpose of integration/differentiation??

Hmm
I used the calculus in optimisation problems in progamming and I understand why.
But currently I'm doing my internship and I was told that I need to do integration but I don't understand why (I'll probably just end up asking my supervisor :/ ).
Also, sometimes the integration needs to be done but I don't know that I should do it...
That's why I'm asking. It's really annoying. I cannot solve a problem if don't know what to use...
cka
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### Re: purpose of integration/differentiation??

What kind of internship?

Is your problem that you don't know if you should integrate OR differentiate, or that you don't know HOW to integrate?

The Chaz
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### Re: purpose of integration/differentiation??

Sir Isaac Newton's main motivation for inventing the calculus was so that he could use his laws of motion and gravitation to mathematically describe a dynamic universe. He converted physics from a science of explanation to a general mathematical system. The vast majority of science would be unapproachable without calculus.

When asked by friends and family what calculus is used for, I tell them to describe anything that changes.

MarkFL
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### Re: purpose of integration/differentiation??

my problem is usually that I don't know if I should integrate.

When it comes to differentiation I can usually tell if I should do it coz I used it in optimisation/neural networks/etc (in artificial intelligence). So usually I can identify when to use differentiation. (Still I would like to know some other real world applications of it - some other examples)

But I always had problem with identifying when I should use integration.
I finally asked my supervisor why I have to use integration and he explained it to me. And, also, when we need to use it. So the problem solved.

@The Chaz -> In my case it was about amount of energy stored in battery.

EDIT:
There are some examples here: