Midpoint Rule

  • Midpoint rule for single integrals
  • Develop the rule for double integrals - example

The midpoint rule is an approximation method for integrals, its a member of 3 different approximation methods, named right endpoint, midpoint, and left endpoint rules).

You can read more about these rules in mat1225notes_written.

Midpoint Rule for Double Integrals

This method works by first dividing the region, , into smaller rectangles and then finding the distance from the center point of the smaller rectangle to the point given by the function above that region. That distance is then used to calculate the volume of a rectangle, thus estimating the integral.

where is the midpoint of and is the midpoint of .

  • - the area of the smaller rectangles
  • - x side length of the smaller rectangles
  • - y side length of the smaller rectangles

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