I was not exactly sure what to title this question, but I would appreciate if someone can confirm my understanding of the left hand, right hand, trapezoidal, midpoint, and simpsons approximations.
It is my understanding that if the Curve is INCREASING:
Left Hand Approximation: Underestimates
Right Hand Approximation: Overestimates
DECREASING:
Left Hand Approximation: Overestimates
Right Hand Approximation: Underestimates
CONCAVE UP:
Midpoint Approximation: Underestimates
Trapezoidal Approximation: Overestimates
CONCAVE DOWN:
Midpoint Approximation: Overestimates
Trapezoidal Approximation: Underestimates
I am not sure of any rules like these exist for Simpson's rule, so if you could inform me if there is a simple trick, as well as confirm my understanding of these approximations and if the rules are true. Thank you.