1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Given two integrals find the third

  1. Nov 22, 2013 #1

    Qube

    User Avatar
    Gold Member

    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. jcsd
  3. Nov 22, 2013 #2

    Simon Bridge

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    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?
     
  4. Nov 22, 2013 #3

    Qube

    User Avatar
    Gold Member

    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.
     
  5. Nov 22, 2013 #4

    Simon Bridge

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Everybody does that at least once :)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted