PPT-Discuss how you would find the area under this curve!

AP Calculus Unit 5 Day 2 APROXIMATE Area under a Curve We will introduce some new Calculus concepts LRAM RRAM MRAM Rectangular Approximation Method RAM to estimate area under curve Example Problem. Cartesian, Parametric, and Polar. Arc Length. x. k-1. x. k. Green line = . If we do this over and over from every . x. k—1 . to any . x. k. , we get . Arc Length. If we make . x. infinitely small, we have the Riemann Sum. Find the area of the given sector:. Slopes and Planar Areas of Polar Curves. Section 10.6a. Finding the Slope of a Polar Curve. The slope of is given by . Observe…. First, conceptualize the curve parametrically:. Area Enclosed Parametrically. Suppose that the parametric equations . x = x(t) . and . y = y(t). with . c .  t  d. , describe a curve that is traced out . clockwise. exactly once, as . t . increases from . Click the mouse button or press the Space Bar to display the answers.. Statistics are from ______ and parameters are from ________. In a uniform distribution everything is ______ likely.. If a distribution is skewed right, which is greater, the mean or the median and why?. Riemann Sums. -Left, Right, Midpoint, Trapezoid. Summations. Definite Integration. We want to think about the region contained by a function, the x-axis, and two vertical lines x=a and x=b. . a. 6. Shane Murphy. s.murphy5@lancaster.ac.uk. Office Hours: Monday 3:00-4:00 – LUMS C85. LUMS . Maths. and Stats Help (MASH) Centre. Are you mystified by . maths. ? Stuck with statistics? The LUMS . Integrate the two parts separately:. Shaded Area =. Integrating with Respect to . y. Section 7.2b. Integrating with Respect to . y. Sometimes the boundaries of a region are more easily. described by functions of . i. n the (. x,y. ). plane. Introduction. This chapter focuses on . P. arametric equations. Parametric equations split a ‘Cartesian’ equation into an x and y ‘component’. They are used to model projectiles in Physics. Area Under a Curve . Using Riemann Sum. Tanya . Fraile. Level: Calculus II. History. 35-acre landscape park in the heart of the City of Newburgh. Designed Calvert Vaux (who also designed Central Park. Section 7.2a. Area Between Curves. Suppose we want to know the area of a region that is bounded. above by one curve, . y. = . f. (. x. ), and below by another, . y. = . g. (. x. ):. a. b. Upper curve. 4-2. . Arc length. Arc Length. Using . P. ythagorean theorem. Arc length. 1) Find the integral for the length of the curve over [0, 2]. . . Find the length of the curve . . from x = 0 to x = 4. shape.. How could we find the volume of this cone?. Example. One way would be to cut it into a series of thin slices (flat cylinders) and add their volumes.. The volume of each flat cylinder (disk) is:. richj@udel.edu. 302.831.7226. Three Examples. Central Banking Policy. Software integrated lecture . for students to understand the effects of central banking policy and to observe the impact on . markets currently and historically. IB Mathematical Studies Standard Level: For the IB diploma (International Baccalaureate).   by Peter Blythe, Jim . Fensom. , Jane Forrest and Paula Waldman De . Tokman. (26 Jul 2012). . Information from this book has been used in this PowerPoint..