Painting a Point

Accumulation 7: An application (of paint) Suppose you started with a point, the origin to be specific, and painted it. You put on layers and layers of paint until your point grows to a sphere with radius r. Let’s stop and admire your work part way through the job; at this point the radius is…

Volumes of Revolution

Applications of Integration 3 – Volumes of Rotation In out last post we discussed volumes of figures with regular cross sections. Many common figures can be analyzed as some region being rotated around a line, possibly one of its edges. For example, the region between the x-axis and the segment with equation  from x =…

Volume of Solids with Regular Cross-sections

Applications of Integration 2 – Solids with Regular Cross-sections In Vino Veritas. And not only truth, but the start of an important application of the calculus. After Johannes Kepler’s (1571–1630) first wife died he decided to marry again. Naturally, he bought wine for the festivities. There was some disagreement with the wine merchant concerning how he…