Chapter 17 Section 17.4 The Double Integral as the Limit of a Riemann Sum; Polar Coordinates.

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Presentation transcript:

Chapter 17 Section 17.4 The Double Integral as the Limit of a Riemann Sum; Polar Coordinates

y x Polar coordinates are used to describe curves that have complicated rectangular equations and make them simpler (at least from a calculus perspective (i.e. integrating)). Circles centered at the origin. Cardioid. 3 leafed rose. Spiral.

Integrating factor (Do not forget!) x y

First graph the region and find the angles where the curves intersect.

Example Sometimes you might need to convert a rectangular integral to polar like the integral to the right. First graph the region.