Hello

Question:

Prove that if f&g are continous and inverse functions for each other and a&b are constant where b>a .. then :

$\displaystyle \int_a^b f(x) \, dx= b f(b) - a f(a) - \int_{f(a)}^{f(b)} g(x) \, dx$

My FAILED try:

Am thinking about a substitution which makes the f(x) be g(x)

So I substitute x=g(g(x)) ..

But this failed; since dx will be compliacted

Any ideas?