# GeoGebra

## Integral

• Visual Display of Simpson's Rule Draws parabolas and shades each area under the parabolas to demonstrate Simpson's approximation rule for Integration, by Eric Funke
• A Demonstration of the Riemann Sum Draws rectangles based on left, mid, right, upper, lower, and random sample points. Compares Riemann sum approximation with the "true" value of the integral. By Marc Renault

• Solids of Rotation Sketches a 3D rotation of curves over a horizontal line, by Eric Funke

• 3D Rectangles and Circles Watch the rectangles and circles pop out of the graph! Grab the Red dashed lines to change a and b, move the sliders and see what happens! The height only applies to the rectangles. By David Sankey

• Riemann Animations Left hand, right hand and trapeziods, and animate everything in between! How could you find the midpoints? Simply grab the red dashed lines to change a and b. By David Sankey

• Area Between Curves Download Given the two functions f(x)=c(x-x1)(x-x2)(x-x3)(x-x4) and g(x)=0.6x+constant , we visualize the area surrounded by the two curves y=f(x) and y=g(x) and the vertical lines through the ends of the interval [a, b]. You can study different cases by changing the x-intercepts and the coefficient of f(x), by dragging y=g(x), and the ends of the interval. The area for each interval and the total area are calculated in a spreadsheet. The value of the definite integral of the difference f(x)-g(x) on the interval [a,b] is given in cell B10 for comparison with the area between the curves. By Irina Boyadzhiev

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