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: Anirudh's Apostol Calculus Problems thread

  1. Jul 22, 2008 #1
    Some time back I made a thread saying I would be buying a calculus book. I ended up buying Apostol as the Indian edition is only 6$. I have made a thread about this because I can see that there are going to be lots of problems I cannot do and I haven't a solution manual.

    1.[tex]\int[/tex] (a2 - x2)ndx

    2. I am supposed to use integration by parts to do this sum.

    3. Using integration by parts,

    x(a2 - x2)n + n[tex]\int[/tex]2x2(a2 - x2)n-1

    But he gets a different answer which is

    [x(a2 - x2)n + 2a2n[tex]\int[/tex](a2 - x2)n-1 dx ]/ 2n+1 + C
    Last edited: Jul 22, 2008
  2. jcsd
  3. Jul 22, 2008 #2


    User Avatar
    Science Advisor

    HOW did you do the integration by parts? What did you use for u and dv?
  4. Jul 22, 2008 #3
    U = (a2- x2)n
    V = x

    I missed an n in the original equation after the integral. OK. Now what?
  5. Jul 22, 2008 #4
    OK. I worked backwards and solved it. But keep this thread open. I shall post any other exercises I have problems with.
  6. Jul 28, 2008 #5
    A function f, continuous on the positive real axis, has the property that for all choices of x>0 and y>0, the integral
    is independent of x (and therefore depends only on y). If f(2) = 2, compute value of integral A(x) = [tex]\int[/tex][tex]^{x}_{1}[/tex]f(t)dt for all x>0
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook