MATH-M 212 Lecture Notes - Lecture 25: Polar Coordinate System, Petal
Document Summary
Section 10. 5 notes- area and arc length in polar coordinates. Recall area under curve- rectangles/riemann sums to estimate; with polar, use sectors of circles o. Sector area: as angle changes, sum of sector becomes, symmetry of graphs often used, integral doubled to cancel out, sectors based on origin, infinite number of ways to find areas. Theorem 10. 13- area in polar coordinates: if is continuous and nonnegative on , where , then the area of the region bounded by the graph of between the radial lines and is given by. Note: will be allowed calculator on test, but know how to evaluate integrals by hand- at least 1 required by hand. Find the area inside 1 petal of . o: all petals equal area; can use any part, going from to gives top half of right petal; double for whole o. Find the area between the loops of . o: big loop:
