PPT-Section 4.3 – Riemann Sums and Definite Integrals

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 ab into N subintervals. 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.. Ms. . Battaglia. – . ap. calculus . Definite integral. A definite integral is an integral . with upper and lower bounds. The number a is the . lower limit. of integration, and the number b is the . 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. 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!!!. Calculus. Calculus answers two very important questions.. The first, how to find the instantaneous rate of change, we answered with our study of derivatives. The second we are now ready to answer, how to find the area of irregular regions.. 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. Section 6.1. Volumes Using . Cross-Sections. Section 6.2. Volumes Using Cylindrical Shells. Section 6.3. Arc Length. Section 6.4. Areas of Surfaces of Revolution. Section 6.5. Work and Fluid Forces. Section 6.6. Area and Estimating with Finite Sums. Section 5.2. Sigma Notation and Limits of Finite Sums. Section 5.3. The Definite Integral. Section 5.4. The Fundamental Theorem of Calculus. 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. ECE 6382 . . Notes are from D. . R. . Wilton, Dept. of ECE. 1. . David . R. . Jackson. . Fall 2017. Notes 10. Brief Review of Singular. . Integrals. Logarithmic . singularities are examples of . integrable. 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. In this Chapter:. . 1 . Double Integrals over Rectangles. . 2 . Double Integrals over General Regions. . 3 . Double Integrals in Polar Coordinates. . 4 . Applications of Double Integrals. . 5 . Triple Integrals.