10680
EXPLORE
LATEST
ABOUT
AUTHORING AREA
PARTICIPATE
Your browser does not support JavaScript or it may be disabled!
The Trapezoidal Rule for Increasing Functions
Let
be a partition of
, with
; then:
≈ the sum of the rectangle areas + the sum of the triangle areas =
.
Contributed by:
Soledad Mª Sáez Martínez
and
Félix Martínez de la Rosa
THINGS TO TRY
Rotate and Zoom in 3D
Gamepad Controls
SNAPSHOTS
DETAILS
Reference:
J. Urias, "Proof without Words: The Trapezoidal Rule (for Increasing Functions),"
Mathematics Magazine
,
68
(3), 1995 p. 192.
RELATED LINKS
Trapezoidal Rule
(
Wolfram
MathWorld
)
PERMANENT CITATION
"
The Trapezoidal Rule for Increasing Functions
" from
the Wolfram Demonstrations Project
http://demonstrations.wolfram.com/TheTrapezoidalRuleForIncreasingFunctions/
Contributed by:
Soledad Mª Sáez Martínez
and
Félix Martínez de la Rosa
Share:
Embed Interactive Demonstration
New!
Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site.
More details »
Download Demonstration as CDF »
Download Author Code »
(preview »)
Files require
Wolfram
CDF Player
or
Mathematica
.
Related Demonstrations
More by Author
Numerical Integration using Rectangles, the Trapezoidal Rule, or Simpson's Rule
Bartosz Naskrecki
Visual Proof of Two Integrals
Soledad Mª Sáez Martínez and Félix Martínez de la Rosa
Visual Computation of an Integral (II)
Soledad Mª Sáez Martínez and Félix Martínez de la Rosa
A Visualization of Logarithms
Soledad Mª Sáez Martínez and Félix Martínez de la Rosa
Visual Computation of an Integral
Soledad Mª Sáez Martínez and Félix Martínez de la Rosa
Numerical Integration: Romberg's Method
Eugenio Bravo Sevilla
Numerical Integration Examples
Jason Beaulieu and Brian Vick
Using Sampled Data to Estimate Derivatives, Integrals, and Interpolated Values
Robert L. Brown
Integration by Riemann Sums
Jiwon Hwang
Finding the Area of a 3D Surface with Parallelograms
Mark Peterson
Related Topics
Approximation Methods
Area
Calculus
Integrals
High School Calculus and Analytic Geometry
High School Mathematics
Browse all topics
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to
Mathematica Player 7EX
I already have
Mathematica Player
or
Mathematica 7+