Given two integrals find the third

[Qube]

Homework Statement

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?

Homework Equations

FTC.

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)?

 

[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?

 

[Qube]

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.

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.

 

[Simon Bridge]

Everybody does that at least once :)