Sometimes you will have integrals that approach asymptotes for certain limits and these may be convergent or divergent. The following two tutorials discuss this by considering the following examples.

Convergent Integrals

Examples:

  1. \text{Evaluate } \displaystyle\int\limits_0^\infty  {e^{-x}{\rm{ }}} dx
  2. \text{Evaluate } \displaystyle\int\limits_{0}^{2}  {\dfrac{1}{\sqrt x}{\rm{ }}} dx
Convergent Integrals : ExamSolutions Maths Revision - youtube Video

Divergent Integrals

Example:

  1. \text{Evaluate } \displaystyle\int\limits_{2}^\infty  {\dfrac{1}{\sqrt x}{\rm{ }}} dx
Divergent Integrals : ExamSolutions Maths Revision - youtube Video