left-endpoint approximation
[left-endpoint approximation|left-endpoint approximation] A left-endpoint approximation is a Riemann sum using the function value at the left endpoint of each subinterval.
Definition
left-endpoint approximation A left-endpoint approximation is a Riemann sum using the function value at the left endpoint of each subinterval. It is calculated for f(x) = sinx over [1,2] with n=4, yielding an approximation of 1.75.
Mechanism
left-endpoint approximation Using a left-endpoint approximation, the heights are f(0) = 0, f(0.5) = 0.25, f(1) = 1, f(1.5) = 2.25. On each subinterval [x_{i-1}, x_i], construct a rectangle with width Δx and height equal to f(x_{i-1}), which is the function value at the left endpoint of the subinterval.
Constraints
left-endpoint approximation The left-endpoint approximation and right-endpoint approximation are two methods examined next. These methods are constrained by their use of endpoint values for estimation.