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I've three functions: f(x), g(x) and h(x). How do I find the area they enclose?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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**ElainaVW****Member**- Registered: 2013-04-29
- Posts: 291

Hello:

I guess that a question phrased like that would get many down votes at the SE.

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But this is not SE!

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,340

Sketch them (good practice for any integration anyway). Then find where they intersect. Then adopt a strategy for getting the area you want.

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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So, there is no magical formula?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,394

Is the simplest idea for between two functions provided f(x) is the function on top.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,340

hi Agnishom,

These three functions may show you the difficulty coming up with a single formula.

1 is sin(x)

2 is 2sin(x)

3 is (x-1.5)^2

The enclosed area would be

difference between 2 and 3 in the region a to b

difference between 2 and 1 in the region b to c

difference between 2 and 3 in the region c to d.

Until you know those crossing points you cannot decide the values of a, b, c and d.

And a small change in one function would change everything.

Bob

*Last edited by bob bundy (2014-06-29 19:19:07)*

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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Okay. So what should have been my question?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,394

Post a problem.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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I do not have any

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,394

What inspired the original question?

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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The rhombus area problem

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,394

I am sorry, I do not remember it.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**αβγ****Member**- Registered: 2014-09-02
- Posts: 19

You can't really use a magical formula to obtain the answer easy peasy because you have 3 functions, each with their own graph. Since I don't know how the graphs are oriented and how they intersect, the only actual answer without anymore information would be the sum of the negative or positive of each integral of each function, i.e.:

That's the most precise answer (in reduced form) that can be obtained without further information.

α as in alpha stands for "**a** love of math"

β as in beta stands for "**b**eing skilled in the latter"

γ as in gamma stands for "**g**etting sick of homework"

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