• Integration by Trig Substitution:

      If the integral contains trig expressions, try substituting some of the basic trig identities:

             

      If the integral contains the sum or difference of two squares, set up right triangles and

         make appropriate trig substitutions.                                 

  • Numerical Integration: When symbolic methods fail, use of some numerical approximation method will give useful answers along a specified interval. Most calculators enact these methods to give extremely exact answers by using very tiny subdivisions.
    • Riemann Sums with Rectangles: Rectangular Approximation Method.
    • Trapezoidal Rule: Trapezoidal approximation.