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25.3 Integrating Inverse Functions

If you can integrate f(x), you can integrate its inverse function as well.

You have:

                            A1       +    A2         = A3 - A4                                          

This can be seen to hold from the pictures, in which f(x) must be an increasing or decreasing function of x. (the inverse is not well defined unless f is one or the other.). Suppose f is increasing.