Processing math: 100%

HW1024

First, watch this Khan Academy Video where Sal discusses how to integrate using polar coordinates. In particular, he shows that the differential element of area in polar coordinates is dA=12r2dθ. Then prove, using integration with polar coordinates, that the area of a semi-circle is πr2 and that ˉy=4r3π.

Hints:

  1. The equation of a circle with radius r in polar coordinates is r(θ)=r.
  2. The process to find area and centroids is exactly the same as previous problems, only the form of the integrals is different.
  3. Finding the area of a circle using polar coordinates is trivially easy.
  4. To find Qx you will need to determine ˉyel as a function of r and θ.
diagram