Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Function of several real variables wikipedia , lookup
Partial differential equation wikipedia , lookup
History of calculus wikipedia , lookup
Riemann integral wikipedia , lookup
Path integral formulation wikipedia , lookup
Fundamental theorem of calculus wikipedia , lookup
AP Calculus BC Chapter 4 – Integration DATE W, 11-9 SCORE LESSON/ASSESSMENT Objectives Th, 11-10 F, 11-11 Write the general solution of a differential equation. Use indefinite integral notation for antiderivatives. Use basic integration rules to find antiderivatives. Find a particular solution of a differential equation. Use sigma notation to write and evaluate a sum. Understand the concept of area. Approximate the area of a plane region. Find the area of a plane region using limits. Objectives Tu, 11-15 W, 11-16 Th, 11-17 Page 255: 9-42 mo3 Page 255: 59, 64, 70, 78, 81-84, 90-97 How is the limit process used to find area under a curve? Page 267: 10, 11, 21, 27, 33 Page 267: 37, 57-69 mo3, 73, 81-88 4.3 Riemann Sums and Definite Integrals Essential Question Understand the definition of a Riemann sum. Evaluate a definite integral using limits. Evaluate a definite integral using properties of definite integrals. Objectives Why must an antiderivative include a constant of integration? 4.2 Area Essential Question Objectives M, 11-14 4.1 Antiderivatives and Indefinite Integration Essential Question HOMEWORK What is the difference between a definite integral and an indefinite integral? Page 279: 3, 4, 1545 mo3, 47, 48, 52, 57, 65-70 4.4 The Fundamental Theorem of Calculus Essential Question Evaluate a definite integral using the Fundamental Theorem of Calculus. Understand and use the Mean Value Theorem for Integrals. Find the average value of a function over a closed interval. Understand and use the Second Fundamental Theorem of Calculus. Understand and use the Net Change Theorem. What are the guidelines for using the Fundamental Theorem of Calculus? Page 293: 6-39 mo3, 51, 53-60 Page 293: 66, 67, 73, 81-92, 94, 97109 odd, 113, 114 F, 11-18 M, 11-21 Tu, 11-22 Objectives M, 11-28 Tu, 11-29 4.1-4.4 Test Review Study for Test 4.1-4.4 Test Part I Study for Test 4.1-4.4 Test Part II None 4.5 Integration by Substitution Essential Question Use pattern recognition to find an indefinite integral. Use a change of variables to find an indefinite integral. Use the General Power Rule for Integration to find an indefinite integral. Use a change of variables to evaluate a definite integral. Evaluate a definite integral involving an even or odd function. W, 11-30 F, 12-2 M, 12-5 Tu, 12-6 Page 306: 12-39 mo3, 48-66 mo3, 67 Page 195: 37, 41, 61, 66, 68, 70, 9194 4.1-4.5 Stations Objectives Th, 12-1 What are the guidelines for making a change of variables for indefinite integrals and definite integrals? Complete Stations 4.6 Numerical Integration Essential Question Approximate a definite integral using the Trapezoidal Rule. Approximate a definite integral using Simpson’s Rule. Analyze the approximate errors in the Trapezoidal Rule and Simpson’s Rule. When would the Trapezoidal Rule be used? Page 316: 3-18 mo3 (Trapezoidal Rule only), 39(a), 46(a), 52 Chapter 4 Stations Study for Test 4.5-4.5 Test I Study for Test 4.5-4.6 Test II None