MAT 1226 Calculus II Section 10.4 Areas and Length in Polar Coordinates

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MAT 1226 Calculus II Section 10.4 Areas and Length in Polar Coordinates

Classroom swap this week... Wednesday – no class if we finish everything today RF – switch to OMH 245

HW… WebAssign 10.4 (17 problems, 151 min.) Do your HW ASAP. Do not wait until Wednesday or Thursday to do your HW. Quiz 02: 10.3, 10.4 –Make sure you understand how to do all the problems, not just the easy one

Preview Area: Regions defined by polar equations is different from the regions defined by rectangular equations Derive the formula Examples Arc Length (from section 10.2)

Common Assumptions It is a custom to assume the obvious geometric symmetries in regions defined by polar equations

To Save Time… We are going to focus on setting up the integral. We will not actually do all computations.

Recall: Riemann Sum i th subinterval sample point

Recall: Riemann Sum

Area

Example 1 Find the area enclosed by one loop of

Example 1

Example 2 Find the area of the region that lies inside and outside

Example 2

Arc Length

Arc Length 1st Formula (10.2, 2 derivatives)

Arc Length 2nd Formula (1 derivative)

Example 3 Find the length of

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