9814
EXPLORE
LATEST
ABOUT
AUTHORING AREA
PARTICIPATE
Your browser does not support JavaScript or it may be disabled!
Visual Proof of Two Integrals
Left graphic:
= blue area + orange area =
.
Therefore
.
Right graphic:
= blue area + orange area =
.
Therefore
.
Contributed by:
Soledad Mª Sáez Martínez
and
Félix Martínez de la Rosa
SNAPSHOTS
DETAILS
Reference: Thomas J. Osler, "Visual Proof of Two Integrals,"
The College Mathematics Journal
,
34
(3), 2003 pp. 241–242.
RELATED LINKS
Integral
(
Wolfram
MathWorld
)
PERMANENT CITATION
"
Visual Proof of Two Integrals
" from
the Wolfram Demonstrations Project
http://demonstrations.wolfram.com/VisualProofOfTwoIntegrals/
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
Visual Computation of an Integral
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
Integration by Riemann Sums
Jiwon Hwang
Numerical Integration using Rectangles, the Trapezoidal Rule, or Simpson's Rule
Bartosz Naskrecki
The Trapezoidal Rule for Increasing Functions
Soledad Mª Sáez Martínez and Félix Martínez de la Rosa
Visualizing Euler's Constant
Soledad Mª Sáez Martínez and Félix Martínez de la Rosa
Two Integral Mean Value Theorems of Flett Type
Soledad María Sáez Martínez and Félix Martínez de la Rosa
Soap Film between Two Equal and Parallel Rings
S. M. Blinder
The Polar Planimeter
Bruce Atwood (Beloit College) and Stan Wagon (Macalester College)
Related Topics
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+