rsums

Interactive evaluation of Riemann sums

Syntax

rsums(f)

rsums(f,a,b)

rsums(f,[a,b])

Description

rsums(f) interactively approximates the integral of f(x) by middle Riemann sums for x from 0 to 1. rsums(f) displays a graph of f(x) using 10 terms (rectangles). You can adjust the number of terms taken in the middle Riemann sum by using the slider below the graph. The number of terms available ranges from 2 to 128. f can be a character vector or a symbolic expression. The height of each rectangle is determined by the value of the function in the middle of each interval.

rsums(f,a,b) and rsums(f,[a,b]) approximates the integral for x from a to b.

Examples

Approximate Integral by Riemann Sum

Approximate the integral ${\int }_0^1{\mathit{x}}^2\mathrm{dx}$ by middle Riemann sum. rsums displays a graph of $$x^2$$ using 10 terms of the midpoint Riemann sum for the integration range from 0 to 1. The total sum is 0.3325.

syms x
rsums(x^2)

Change the integration range of $$x$$ from -2 to 5. The total Riemann sum is 44.0475.

rsums(x^2,-2,5)

Input Arguments

f — Integrand

symbolic expression | symbolic function | symbolic number

Integrand, specified as a symbolic expression, function, or number.

a — Lower bound

number | symbolic number

Lower bound, specified as a number or symbolic number.

b — Upper bound

number | symbolic number

Upper bound, specified as a number or symbolic number.

Version History

Introduced before R2006a