A REA AND A RC L ENGTH IN P OLAR C OORDINATES Section 10-5.

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Presentation transcript:

A REA AND A RC L ENGTH IN P OLAR C OORDINATES Section 10-5

Area in Polar Coordinates The area of the region bounded by the curve between the radial lines And is given by: Handout 10-5 with proofs

1) Find the area of the region in the plane enclosed by Graph (polar) to find the two radial lines which form the region

1) cont’d

2) Find the area inside the smaller loop of the limacon

2) cont’d

3) Sketch and set up an integral expression of the area of one petal of

The length of the curve as Is given by: Arc Length of Polar Curves

4) Find the length of the arc from for the cardioid

4) cont’d

5) Find the length of the arc from for using calculator to integrate

H OME W ORK Page 747 # 1-4, 7, 9, 11, 14, 25, 26, 27, 28, 29, 58, 60, 61, 63, 65