4.8/

Approximating Double Integral

1. What?
2. Why?
3. Comoposite Trapezoidal Rule for Double Integral:
   \(\ \ \iint_R f(x,y) \,dA \ =\) \(\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\)
   • DERIVATION:
4. Comoposite Simpsons’ Rule for Double Integral:
   
   • Rule:
   • Error:
   • Derivation:

Gaussian Quadrature for Double Integral Approximation

1. What?
2. Why?
3. Example:
   

Non-Rectangular Regions

1. What?

   Form:
   

   
   or,
   

2. How?
   
   • We use
   • Step Size:
     • x:
     • y:
3. Simpsons’ Rule for Non-Rect Regions:
   
4. Simpsons’ Double Integral [Algorithm]:
   
5. Gaussian Double Integral [Algorithm]:
   

Triple Integral Approximation

1. What?

   • On what?

   • Form:

2. Gaussian Triple Integral [Algorithm]: