Finding definite integral of f(x) but not given a function?

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May 1st 2009, 02:24 PM
ceb0196

Finding definite integral of f(x) but not given a function?

I think my prof is trying to trip me up. Here is the question(sorry, I don't know the codes to make it in the right form):

Suppose: integrand with b=6 and a=1 of f(x) dx=9, integrand with b=4 and a=6 of f(x) dx=4, then find integrand with b=4 and a=1

does that make any sense? How do I solve this without being given a function??
May 1st 2009, 02:27 PM
mr fantastic

Quote:

Originally Posted by ceb0196

I think my prof is trying to trip me up. Here is the question(sorry, I don't know the codes to make it in the right form):

Suppose: integrand with b=6 and a=1 of f(x) dx=9, integrand with b=4 and a=6 of f(x) dx=4, then find integrand with b=4 and a=1

does that make any sense? How do I solve this without being given a function??

You're given $\int_1^6 f(x) \, dx = 9$ and $\int_4^6 f(x) \, dx = 4$ .

Note that $\int_1^6 f(x) \, dx = \int_1^4 f(x) \, dx + \int_4^6 f(x) \, dx \Rightarrow \int_1^4 f(x) \, dx = \int_1^6 f(x) \, dx - \int_4^6 f(x) \, dx$ .
May 1st 2009, 02:32 PM
Plato

Is this your question: $\int_1^6 f = 9\;\& \;\int_6^4 f = 4\; \Rightarrow \;\int_1^4 f = ?$ ?

If so, notice that $\int_4^6 f = - 4\;\& \;\int_1^4 f + \int_4^6 f = \int_1^6 f$ .
May 1st 2009, 02:35 PM
ceb0196

Yes, that is the question. Thanks to both for the start; I will try to work it out!
May 1st 2009, 02:52 PM
ceb0196

I just can't figure out what I am missing. How do I solve without having a function that I can plug F(b) and F(a) into??
May 1st 2009, 02:58 PM
mr fantastic

Quote:

Originally Posted by ceb0196

I just can't figure out what I am missing. How do I solve without having a function that I can plug F(b) and F(a) into??

Read posts #2 and #3 again. Read them carefully. Where is your trouble in plugging in the value of things that you know and solving for the thing that you don't know?
May 1st 2009, 03:14 PM
ceb0196

Is it 13? It can't possibly be that simple...
May 1st 2009, 03:26 PM
Plato

Quote:

Originally Posted by ceb0196

Is it 13? It can't possibly be that simple...

Oh yes, it is indeed that simple!
May 1st 2009, 03:36 PM
ceb0196

Oh my goodness gracious. Thanks to all of you for helping me fumble through the last week of this class!