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# Application of Integration

Posted on 2011-03-19
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Hi experts,
What is the application of integral calculas. Where to use integration in realtime.

Regards,
Vimal.
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Question by:vimalalex

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Expert Comment

An example from physics: if you integrate your acceleration over time you receive your speed (given some initial speed). Integration of speed gives you the way you moved from a certain starting point.
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Expert Comment

Let's say I'm making gas tanks for automobiles. I want the guage that says how much is left to be accurate, but the tank isn't a cube of course. How do I map the height of the fuel in the tank to a number of gallons? This could be solved with calculus easily.
Also, if you want to build a swimming pool and would like to know how much pressure would be on the sides of the pool when full, you would need an integral.
Basically anything that operates over an area or an odd shape needs integrals.
Technically, no one would even know the exact formula for the volume of a sphere or a cone if someone hadn't used an integral to solve it at some point.
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Expert Comment

..although the volume of a sphere was derived by Archimedes, two thousand years before the formal existence of integration.
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Expert Comment

True, but that's what he used (well, I believe technically he used what we would call Riemann sums to get the cone volume and some fancy trickery from there, but it's the same thing).
You could figure it out by submerging it in water too (another trick good old Archimedes used), but for a rigorous proof, you need calculus.
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Author Comment

Hi All,
Please give me some example using step by step solving of some problems through integral formulas.

Regards,
Vimal.

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Expert Comment

If you just Google for "applications of integrals" you will get even more examples of problems.
This gives some simple examples with solutions.
http://mathpost.asu.edu/~vicki/Integration.htm
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Accepted Solution

InfoStranger earned 250 total points
Let me give you a different example than the one I gave in the differential question.

Keep in Mind Statistics uses integration and differentials all the time.  Statistics is used to explain patterns through formulas.

Let's simplify again but not too much.  Integration is about continuous data.  Take for example coin flipping.

1 flip is known as a Bernoulli distribution
multiple flips of the coin that is countable is the Binomial Distribution
If you continually flip a coin, you will have the Normal Distribution

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Author Comment

Hi InfoStranger,
Can u pls solve the above using Integration formulas.

Regards,
Vimal.
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LVL 37

Expert Comment

vimalalex, I think we are having trouble giving you what you want because we don't understand what you need.
Are you looking for us to work out some basic calculus proplems for integration like "Find the indefinite integral of x^2-x+2" or are you looking for examples of practical applications for integrals (which have been given)?
Can you please be specific in what you are looking for. What types of problems, etc? Give examples maybe. There are many different types of these problems with many different levels of difficulty.
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Author Comment

Hi TommySzalapski,

I mean, I am looking for the practical applications for differentiation which you have defined in sentence.

Regards,
Vimal.
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Author Comment

Hi TommySzalapski,

I mean, I am looking for the practical applications for Integration which you have defined in sentence.

Regards,
Vimal.
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LVL 37

Assisted Solution

TommySzalapski earned 250 total points
You can use it to find the area of odd shapes. Let's say you have a trapezoid, the bottom is 8, the top is 2, and the height is 5. Let's also pretend you forgot how to do this with triangles.
The formula for the width at any given height is 8 - 6/5h. So what's the area? Get the integral from 0 to 5.
So 8h - 6/5(h^2)/2 | h = 0 to 5
= 8h - 3/5 h^2 | h = 0 to 5
= 8(5) - 3/5(5)^2 - (8(0) - 3/5(0)^2
= 40 - 15 - 0
= 25
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