Deriving the Integral Property from Theorems 1-45 and 1-46

[Prometheus11]

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, I am using a tablet and the app does not seem to contain buttons for mathematical symbols.

 

[Prometheus11]

Nevermind. Forget this. I got it.

 

[Mark44]

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, I am using a tablet and the app does not seem to contain buttons for mathematical symbols.

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?