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

1. ## 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??

2. 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 $\int_1^6 f(x) \, dx = \int_1^4 f(x) \, dx + \int_4^6 f(x) \, dx \Rightarrow \int_1^4 f(x) \, dx = \int_1^6 f(x) \, dx - \int_4^6 f(x) \, dx$.

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

If so, notice that $\int_4^6 f = - 4\;\& \;\int_1^4 f + \int_4^6 f = \int_1^6 f$.

4. Yes, that is the question. Thanks to both for the start; I will try to work it out!

5. 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??

6. 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?

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

8. Originally Posted by ceb0196
Is it 13? It can't possibly be that simple...
Oh yes, it is indeed that simple!

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