PPT-Approximating the area under a curve using Riemann Sums

Riemann Sums Left Right Midpoint Trapezoid Summations Definite Integration We want to think about the region contained by a function the xaxis and two vertical lines xa and xb a. If ab be a continuous function and 0 then the area of the region between the graph of and the xaxis is de64257ned to be Area dx Instead of the xaxis we can take a graph of another continuous function such that for all ab and de64257ne the area o 4-B. . Exact Area. . . . Use geometric shapes such as rectangles, . circles, trapezoids, triangles etc…. . rectangle. triangle. parallelogram. Approximate Area . . . Midpoint. Sigma Notation. What does the following notation mean?. means. the sum of the numbers from the lower number to the top number.. Area under curves. In 5.1, we found that we can approximate areas using rectangles.. Section 5.2a. First, we need a reminder of . sigma notation:. How do . we evaluate. :. …and what happens if an “infinity” symbol appears. above the sigma???.  The terms go on indefinitely!!!. Ellen, . M. egan, Dan. Riemann Hypothesis. The nontrivial Riemann zeta function zeros, that is, the values of s other than -2,-4,-6….. . s. uch that . δ. (s)=0 all lie on the critical line . Θ. = R[s] = ½ (with real part ½). GIS Application with Web Service Data Access. Introduction – The Problem. Stormwater . utilities are . unique. Runoff can’t be measured. Must be defensible. Impervious area is usually . the . basis for billing. Rizzi – . Calc. BC. The Great Gorilla Jump. The Great Gorilla Jump. Left-Hand Riemann Sum. Right-Hand Riemann Sum. Over/Under Estimates. Riemann Sums Summary. Way to look at accumulated rates of change over an interval. 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. Probability Distribution. Imagine that you rolled a pair of dice. What is the probability of 5-1. ?. To answer such questions, we need to compute the whole population for possible results of rolling two dices. . Riemann Sums. The sums you studied in the last section are called . Riemann Sums. When studying . area under a curve. , we consider only intervals over which the function has positive values because area must be positive. Riemann Sums. a. b. The rectangles need not have equal width, and the height may be . any. value of . f. (. x. ). within the subinterval. .. 1. Partition (divide) [. a,b. ] into . N. subintervals.. Haley Scruggs . 1. st. Period. 3/7/11. A Brief Overview of what Riemann Sums, Trapezoidal Rule and Simpson’s Rule do…. Each of these method estimate the area of a curve using rectangles. . As your number of rectangles increase so does the accuracy of the area. . Cameron Clary. Riemann Sums, the Trapezoidal Rule, and Simpson’s Rule are used to find the area of a certain region between or under curves that usually can not be integrated by hand. .. Riemann Sums. Conceptually the idea of . area. is simply. “. the product of two linear dimensions. ” . The notion of Riemann Sum is then an extension of this idea to more general situations. However, in the formula.