tailieunhanh - Lecture Mathematics 53: Lecture 4.4 - UP Diliman

We now need to move into the Calculus II applications of integrals and how we do them in terms of polar coordinates. In this section we’ll look at the arc length of the curve given by, where we also assume that the curve is traced out exactly once. Just as we did with the tangent lines in polar coordinates we’ll first write the curve in terms of a set of parametric equations. | Area of a Plane Region and Arc Length Mathematics 53 Institute of Mathematics UP Diliman Instituteof Mathematics UP Diliman Area Arc Length Mathematics 53 1 61 For today Area of a Plane Region Arc Length Instituteof Mathematics UP Diliman Area Arc Length Mathematics 53 2 61 Review of Parabolas and Circles Parabolas opening upward or downward o y ax2 bx c parabola with vertex at ac . 2a 4a o a 0 parabola opens upward o a 0 parabola opens downward o y k a x h 2 parabola with vertex at h k a 0 parabola opens upward a 0 parabola opens downward Instituteof Mathematics UP Diliman Area Arc Length Mathematics 53 4 .

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