Multivariable calculus, class #23: Integrals in polar coordinates

Mathematician spotlight: Evelyn Lamb

We give an example of an integral over a disk that is impossible in rectangular coordinates. We derive the integration factor
dA = r * dr * d theta
for polar coordinates, using a picture of a sector of a circle. We successfully compute the integral in polar coordinates. We do two more examples of integrals in polar coordinates. Then we show how to derive the integration factor "r" using the determinant of the Jacobian matrix for the linear transformation from polar coordinates to rectangular coordinates.

[anshukumartiwari]

Good evening mam,
Please post the lectures of linear algebra next . Really enjoying this amazing lectures of yours.

[nicktohzyu]

35:20 that doesn't seem right? You have a circle with radius 0.5, so it has an area of pi/4. How can half that be equal to 1??