Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Integral equation. Please check

  1. Feb 5, 2010 #1
    I have recently been playing with integrals and I still do not fully understand them.

    Usually the best way for me to learn is to play with values and figure it out on my own, so I would like you (physics forum) to check my work so far.

    After a bit of time I got this:

    [tex]\int_{0}^{t}ax^ndx=\frac{at^{n+1}}{n+1}, n\neq-1[/tex]


    and after figuring out:
    [tex]\int_{0}^{t}ax+bxdx=\int_{0}^{t}axdx+\int_{0}^{t}bxdx[/tex]

    I got this equation.

    [tex]\int_{0}^{t}ax^n+bx^{n-1}+cx^{n-2} \cdots +ex dx=\int_{0}^{t}ax^ndx+\int_{0}^{t}bx^{n-1}dx+\int_{0}^{t}cx^{n-2}dx \cdots +\int_{0}^{t}(ex)dx=\frac{at^{n+1}}{n+1}+\frac{bt^n}{n}+\frac{ct^n-1} {n-1} \cdots +et[/tex]

    Is this true for all polynomials (in standard form)? or does it even work at all?
     
    Last edited: Feb 5, 2010
  2. jcsd
  3. Feb 6, 2010 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Hi yyttr2! :wink:

    Yes, that's correct.

    The integral of the sum is the sum of the integrals …

    you can always split a sum (any sum, not just polynomials) into its separate parts, and integrate them separately. :smile:

    (unless, of course, that requires you to add an ∞ and a minus ∞)
     
  4. Feb 6, 2010 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    You can prove, in general, that
    [tex]\int (f_1(x)+ f_2(x)+ \cdot\cdot\cdot+ f_n(x))dx= \int f_1(x)dx+ \int f_2(x)dx+ \cdot\cdot\cdot+ \int f_n(x) dx[/tex]
    by induction on n.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Integral equation. Please check
  1. Please help check work (Replies: 1)

Loading...