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Using the App and Apostol

  1. Dec 2, 2013 #1
    Hello there. I recently installed the Physics Forums app and could not find the homework section in the categories so I beg your pardon from the following question.

    I am using Apostol's Calculus Volume 1 and have encountered a problem on page 72 number 21 (for those in possession of the text). The problem is as follows;

    Derive the following property of the integral as a consequence of theorems 1-45 and 1-46:

    The integral from b to a of f(c-x) dx is equal to the integral from (c-b) to (c-a) of f(x) dx. Pardon me, im using a tablet and the app does not seem to contain buttons for mathematical symbols.
  2. jcsd
  3. Dec 2, 2013 #2
    Nevermind. Forget this. I got it.
  4. Dec 2, 2013 #3


    Staff: Mentor

    In symbols,
    $$\int_b^a f(c - x)dx = \int_{c - b}^{c - a} f(x)dx$$

    If you let u = c - x (from which we get du = -dx), you can rewrite the integral on the left and change the limits of integration. What do you get when you do that?
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