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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


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    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
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