Using the area in polar exploration tool

Notes on the interface

Like the polar plots exploration tool, the area in polar exploration tool allows you to define polar as a function of polar by entering a θ expression in the r = f(θ) =  text input box. The α = and β = text input boxes are, again, for specifying the lower and upper limits on θ for your polar plot. The tool displays a family of sectors whose total area approximates the area of the region -- in other words, the region inside the polar graph within the specified polar angle limits. The number of sectors used can be varied from 1 to 100 using the Number of subdivisions slider. (Of course using more sectors tends to produce more accurate approximations of area.) The radius of each sector is given by the radius function evaluated at a sample polar angle from within the angular interval corresponding to the sector. The Sample point scheme dropdown menu allows you to modify the manner in which sample angles are chosen. (The user should recognize that the Number of subdivisions and Sample point scheme controls provide a specification of a [evenly spaced] partition that gives rise to the Riemann sum used to approximate the region's area.)

After making any changes to the formula for or the values of or you need to click the Process new equation button to update the graphics.

As is the case for many of the tools in this toolkit, the graphics are draggable. The Additional options menu also provides a zoom slider.