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!

Integral area type problem.

  1. Nov 12, 2015 #1
    1. The problem statement, all variables and given/known data
    Find the area of the region between the graphs of: y=x^3+3x^2+5x and y = x^3+2x^2+7x on the interval [-1,2]

    3. The attempt at a solution

    I am not entirely sure what they mean by the REGION between the graphs, is this the region which encloses an area when the two functions cross over each other? not entirely sure what that means. I digress.

    To find where they overlap I set them equal to each other and then isolated one entire side to zero. and got: x^2 - 2x = 0
    So is this like my "main function" that I need in order to find the area. Is this the function that represents the area in between the aforementioned functions? If so, then I'd have to get the area and to get the area of any function I am guessing I'll have to take it's integral and since it's been defined on the interval [-1,2] I use those two points as a and b for my integral.

    Therefore,
    ∫[from -1 to 2] |x^2 - 2x|dx

    I know area is always positive so is it a good idea to always use absolute values when taking a functions integral? And is the dx always needed all the other problems I did seem to use that dx symbol.


    From that point I get a bit stuck as to what to do next

    .
    Please help
    Thank you
     
    Last edited: Nov 12, 2015
  2. jcsd
  3. Nov 12, 2015 #2

    andrewkirk

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    The area between the two curves is positive regardless of which curve is uppermost at any value of x. Hence it is equal to the integral between the two x limits of the absolute value of the difference between the two functions.

    In practice the easiest way to evaluate it is often to break up the integral into parts that run between consecutive crossover points. Evaluate the integral of the difference of the functions over each of those subintervals (don't put absolute value signs inside the integrals), then add up the absolute values of the results.
     
  4. Nov 12, 2015 #3

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    Is there a typo in your second curve y = x^2+2x^2+7? Should that be y = x^3 + 2 x^2 + 7, or should it be y = x^2 + 2x + 7?
     
  5. Nov 12, 2015 #4
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Integral area type problem.
Loading...