Area of Plane Regions Visualization 1
Introduction of the Applet
The region enclosed by x=y^2 and y=x−2 is analyzed using both vertical and horizontal strips. Considering that GeoGebra cannot express functions of x in terms of y, it cannot directly consider horizontal strips. We can instead consider a different orientation to visualize horizontal strips in a vertical manner. This approach provides a way to check our integral calculations interactively and tangibly. We also consider rotation and reflection functionalities to visually prove that the given region is the same as the region of the function with a different orientation.
How to use the applet:
- Move the slider to 270 degrees to align the parabola opening upwards with the parabola opening to the east.
- Manually compute the area of the region by following these steps: a. Determine the functions involved. b. Determine the roots where these functions intersect to identify the boundaries. c. Set the integrand. d. Compute the integral/antiderivative of the integrand using the determined boundaries.
- Input and compute the integrand using the IntegralBetween functionality in GeoGebra, and be amazed at how it coincides with your offline computations.