Help on an integral problem.

Question

anonymous · Answer

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anonymous · Answer

Alright - you want a long explanation on how integrals work in general or a short one on how to solve that problem in particular ?

anonymous · Answer

just a short one will do, I', not sure how to start the problem

anonymous · Answer

*I'm

anonymous · Answer

Well, it starts with how the function is defined. 

f(x) is a function which equals 3 if x is between 4 and 12 and equals -4 if x is between 12 and 20. It's really not a hard thing to imagine:

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anonymous · Answer

4 is positive because $$-\int\limits_{a}^{b} f(x)dx$$ right?

anonymous · Answer

Now, to evaluate the integral between the interval of 4 and 20 might sound a bit tricky at first due to the fact that f(x) can take two different values depending on what x is but you'll see that it's really not. 

To solve this we use one of the properties of the defined integral, which says that:

(Sorry I don't know how to do the integral sign here)

If c is a value between [a.b] and F is a function with its values defined between [a,b] so that
integral of F between a and b exists then 

Integral of F between [a,b] = Integral of F between [a,c] + Integral of F between [c,b].

anonymous · Answer

Oh yeah, sorry about that last bit - I missed the negative in front. It should be:

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