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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'

I'm not crazy, my mother had me tested.

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**ElainaVW****Member**- Registered: 2013-04-29
- Posts: 580

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'

I'm not crazy, my mother had me tested.

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,845

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

Bob

Children are not defined by school ...........The Fonz

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'

I'm not crazy, my mother had me tested.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 108,728

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.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,845

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)*

Children are not defined by school ...........The Fonz

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'

I'm not crazy, my mother had me tested.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 108,728

Post a problem.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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I do not have any

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

I'm not crazy, my mother had me tested.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 108,728

What inspired the original question?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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The rhombus area problem

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

I'm not crazy, my mother had me tested.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 108,728

I am sorry, I do not remember it.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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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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