Approximating the Definite Integral of a Polynomial Using Left-Hand Endpoints
by Mike Martin

On this page, you can vary the number of partitions, N, used to approximate the definite integral for

y = f ( x ) =   a6 x6 + a5 x5 + a4 x4 + a3 x3 + a2 x2 + a1 x + a0

on the interval a < x < b using left-hand endpoints on each subinterval. If the function is non-negative on [a, b], then the definite integral on [a, b] can be interpreted as the area of a region R (the region R being bounded above by the graph of y = f ( x ), below by the x-axis, and vertically by the lines x = a and x = b). Submit real values for all of the parameters to obtain a numeric approximation of the definite integral (area), the error involved, and a visualization of the region with the rectangles used. On this page, the height of the rectangles is determined by utilizing the x-value of the left-hand side of each subinterval.

Enter in the value of the parameters and select the plotting bounds, then press the "Plot/Evaluate" button.

a6 =  

a5 =  

a4 =  

a3 =  

a2 =  

a1 =  

a0 =  

a =  

b =  

N =  

The approximation is

The error in the approximation is


Wikipedia's Definite Integrals

Wikipedia's Numerical Integration

MathWorld's Integral

Wolfram's Integration