# Given two integrals find the third

1. Nov 22, 2013

### Qube

1. The problem statement, all variables and given/known data

The integral of f(x) from 0 to 1 is 3, and the integral of f(x) from 1 to 3 is -2. What is the integral of f(x) from -3 to 3?

2. Relevant equations

FTC.

3. The attempt at a solution

From the equations given I know:

F(1) - F(0) = 3, and

F(3) - F(1) = -2.

How do I find F(3) - F(-3)?

I don't know if the function is symmetrical so that doesn't help.

The closest I can do is solve for F(3). But where do I get F(-3)?

2. Nov 22, 2013

### Simon Bridge

You are correct - there is not enough information presented above.

Consider:$$f(x)=\left \{ \begin{array}{rl} a-1 & :\; x<0\\ 3 & :\; 0\leq x < 1\\ -1 & :\; 1\leq x \end{array}\right.\\ \int_0^1f(x)\;\text{d}x=3\\ \int_1^3f(x)\;\text{d}x = -2$$...fitting the description given, and: $$\int_{-3}^3f(x)\;\text{d}x=a$$...where a can be anything.
There is no unique solution.

You need to look back over the context of the question to see if there is not something that the problem is assuming you already know.
Like, maybe you have been using only certain kinds of functions recently?

3. Nov 22, 2013

### Qube

Oops, missed it! I missed the operative word in the question:

"Now suppose that the integral of .."

The question was part of a series of problems with context provided by previous problems.

4. Nov 22, 2013

### Simon Bridge

Everybody does that at least once :)