1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Range of Integrated function

  1. May 4, 2017 #1
    1. The problem statement, all variables and given/known data
    Let ##g(x) = \int_0^xf(t) dt## where ##f## is such that ##\frac{1}{2} \leq f(t) \leq 1## for ##t \in [0,1]## and ##\frac{1}{2} \geq f(t) \geq 0## for ##t \in (1,2]##. Then ##g(2)## belongs to interval
    A. ##[\frac{-3}{2}, \frac{1}{2}]##
    B. ##[0, 2)##
    C. ##(\frac{3}{2}, \frac{5}{2}]##
    D. ##(2, 4)##

    2. Relevant equations


    3. The attempt at a solution
    I got ##g'(x) = f(x)## and using this and the definite integral given, i have ##g(0) = 0##
    I didn't really know where to go from here, so I tried making a graph (sort of) using the minimum and maximum slopes of the function in the given intervals and found an area in which, I think the function will exist, with the interval for ##g(2)## being ##[\frac{1}{2},\frac{3}{2}]##. ^CEEE41B8BDC6F80CABC7D6937AE5C0255667098491E38C8A1F^pimgpsh_fullsize_distr.jpg
    This isn't present in the options...Can someone please point out my mistakes and help me get the answer.
     
    Last edited: May 4, 2017
  2. jcsd
  3. May 4, 2017 #2

    BvU

    User Avatar
    Science Advisor
    Homework Helper
    2017 Award

    I mostly agree with your reasoning; generally the lower bound of an interval is given first, followed by the upper bound: ##[{1\over 2},{3\over 2}]## is your result. If it isn't in the list litterally, you might try to exclude the answers that certainly don't satisfy...
     
  4. May 4, 2017 #3
    Ah silly me. Will edit it. I found the answer key too and it says B is correct. Is ##g(0) =0## correct?
     
  5. May 4, 2017 #4

    BvU

    User Avatar
    Science Advisor
    Homework Helper
    2017 Award

     
  6. May 4, 2017 #5
    Now I get it! Thank you!
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted