The Relationship Between a Function, a Functions Inverse, and their   Antiderivatives with an Emphasis in Finding Exact Roots with the Technique of   Integration
  Using a new technique involving integration it is possible to find the exact roots of simple functions. In this case, simple functions are defined as smooth functions having an inverse, and that inverse having an antiderivative. This technique now makes it possible to find the exact roots of certain functions without the use of numerical or iterative methods. 
Judah Francis Unmuth-Yockey