Approximating the Definite Integral of a Polynomial Using Trapezoids by Mike Martin

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

y = f ( x ) = a_{6} x^{6} + a_{5} x^{5} + a_{4} x^{4} + a_{3} x^{3} + a_{2} x^{2} + a_{1} x + a_{0}

on the interval a < x < b using trapezoids 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 trapezoids used.

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

a_{6} =

a_{5} =

a_{4} =

a_{3} =

a_{2} =

a_{1} =

a_{0} =

a =

b =

N =

The approximation is

The error in the approximation is

References:

Wikipedia's Definite Integrals Wikipedia's Trapezoidal Rule Wikipedia's Numerical Integration MathWorld's Integral Wolfram's Integration

Wikipedia's Trapezoidal Rule

Wikipedia's Numerical Integration

MathWorld's Integral

Wolfram's Integration