The function is .
Apply derivative on each side with respect to .
From the Fundamental Theorem of Calculus part 1:
\If is continuous on
, then the function
defined by
,
is continuous on
and differentiable on
, and
.
.
Therefore the derivative function is always positive.
\Thus, the function is strictly monotonic and it is an one to one function.
\Find .
From theorem 5.9:
\.
.
Equate to
.
Integral property: .
From the above property we will get .
Therefore, .
.
Substitute in
.
Consider .
.
Substitute in
.
.
.