PPT-2. Definite Integrals and Numeric Integration

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. Under the Modern palette you should find a sub palette called Numeric Within the Numeric palette you will see the first two icons are the Numeric Control and Numeric Indicator These two front panel objects will allow you to manipulate inputs and s integrable. functions. Section 5.2b. Do Now: Exploration 1 on page 264. It is a fact that. With this information, determine the values of the following. integrals. Explain your answers (use a graph, when necessary).. 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 . 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 6.2a. A change of variables can often turn an. unfamiliar integral into one that we can. evaluate…. This method is called the. substitution method of integration.. The New Method. The New Method. Maurits W. Haverkort. Institute for theoretical physics . –. Heidelberg University. M.W.Haverkort@thphys.uni-heidelberg.de. The Coulomb Integral is nasty: . T. he integrant diverges at r. 1. =r. 2. Amadeo Rodgers. Definite Articles . singular . | . plural. La . L. as Feminine. El Los Masculine. Definite Articles Cont.. Most nouns that end in (-o) are masculine. Most nouns that end in (-a) are feminine. continuous. functions over . closed. intervals.. Sometimes we can find integrals for functions where the function . is discontinuous or . the limits are infinite. These are called . improper integrals. 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. As the number of rectangles increased, the approximation of the area under the curve approaches a value.. Copyright .  2010 Pearson Education, Inc.. Section 5.3 – The Definite Integral. Definition. Visualize and compute.  . Solution. . First we graph the function over the interval . using a . grapher. ..  . is the area of the yellow region..  . Now we compute..  .  .  . We’ve learned how to use . Gulf Restoration Network Decision. Nutrients. Nitrogen (N). Phosphorus (P). . Sources include:. NPS: fertilizer/manure runoff, septic tank overflow. Point sources: municipal/industrial wastewater. Using Iterated Integrals to find area. Using . Double Integrals to find Volume. Using Triple Integrals to find Volume. Three Dimensional Space. In Two-Dimensional Space, you have a circle. In Three-Dimensional space, you have a _____________!!!!!!!!!!!. 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..