PPT-Section 5.3 – The Definite Integral

As the number of rectangles increased the approximation of the area under the curve approaches a value Copyright 2010 Pearson Education Inc Section 53 The Definite Integral Definition. 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 . Antiderivative. First let’s talk about what the integral means!. Can you list some interpretations of the definite integral?. Here’s a few facts. :. 1. If f(x) > 0, then returns the . numerical value of the area between. Antidifferentiation. Section 5.3a. Consider the “Do Now”…. What happens to an integral value if we simply . switch. t. he order . of the limits of integration???. If we sum rectangles moving from . 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!!!. FACULTY OF EDUCATION. Mathematics Education Department. Integratıon, fınıte sum and defınıte ıntegral. 1. Orhan TUĞ (PhDc). A. Figure 5.1.8. Figure 5.1.9. Error analysis. Error analysis. Upper and lower estimates of the area. 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.. 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. All graphics are attributed to:. Calculus,10/E. by Howard Anton, Irl Bivens, and Stephen Davis. Copyright © 2009 by John Wiley & Sons, Inc. All rights reserved.”. Introduction. In the last section, we showed how to find the sum of a series by finding a closed form for the nth partial sum and taking its limit.. 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.. 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. Antiderivatives. and Indefinite Integration. Definition of an . Antiderivative. A function F is an . antiderivative. of . f. on an interval I if F’(x) = . f. (x) for all x in I.. Theorem – Representation of . COURSE name : - INTEGRAL CALCULUS . DEPARTMENT OF MATHEMATICS . COURSE CODE :- MATH 309 TH . Course Description. Theorem 1: On Definite Integral . Theorem 2 : On Definite Integral. . Theorem 3 : On Definite Integral.