Presentation is loading. Please wait.

Presentation is loading. Please wait.

AP Calculus BC October 11, 2016.

Published byCassandra Potter Modified over 6 years ago

Similar presentations

Presentation on theme: "AP Calculus BC October 11, 2016."โ€” Presentation transcript:

1 AP Calculus BC October 11, 2016

2 Entry Task ๐‘ฅ+7 ๐‘‘๐‘ฅ ๐‘ฅ+6 ๐‘ฅ ๐‘‘๐‘ฅ sec ๐‘ฆ tan ๐‘ฆ โˆ’ sec ๐‘ฆ ๐‘‘๐‘ฆ
Find the indefinite integral: ๐‘ฅ+7 ๐‘‘๐‘ฅ ๐‘ฅ+6 ๐‘ฅ ๐‘‘๐‘ฅ sec ๐‘ฆ tan ๐‘ฆ โˆ’ sec ๐‘ฆ ๐‘‘๐‘ฆ

3 Learning Targets I understand the definition of a Riemann Sum
I understand how to evaluate a definite integral using limits and properties of definite integrals I can evaluate definite integrals.

4 Evaluating Definite Integrals
Find the integral: โˆ’2 1 2๐‘ฅ ๐‘‘๐‘ฅ Area under the curve

5 Area of common geometric figures
1 3 4 ๐‘‘๐‘ฅ 0 3 ๐‘ฅ+2 ๐‘‘๐‘ฅ โˆ’ โˆ’ ๐‘ฅ 2 ๐‘‘๐‘ฅ

6 Properties of Definite Integrals
๐œ‹ ๐œ‹ sin ๐‘ฅ ๐‘‘๐‘ฅ = ? 3 0 ๐‘ฅ+2 ๐‘‘๐‘ฅ= ? โˆ’ 0 3 ๐‘ฅ+2 ๐‘‘๐‘ฅ = ? โˆ’2 0 ๐‘ฅ 2 ๐‘‘๐‘ฅ ๐‘ฅ 2 ๐‘‘๐‘ฅ = ? โˆ’2 2 ๐‘ฅ 2 ๐‘‘๐‘ฅ= ?

7 Properties of Definite integrals
2 4 4 ๐‘ฅ 2 ๐‘‘๐‘ฅ = ? ๐‘ฅ 2 ๐‘‘๐‘ฅ = ? 1 3 โˆ’ ๐‘ฅ 2 +4๐‘ฅ โˆ’3 ๐‘‘๐‘ฅ = ?

8 Homework #17 ยง4.3 #44, 47, 48, 52

Download ppt "AP Calculus BC October 11, 2016."

Similar presentations

Find the period of the function y = 4 sin x. 1234567891011121314151617181920 2122232425262728293031323334353637383940 41424344454647484950 1. 2. 3.

Find the period of the function y = 4 sin x
Aim: Riemann Sums & Definite Integrals Course: Calculus Do Now: Aim: What are Riemann Sums? Approximate the area under the curve y = 4 โ€“ x 2 for [-1, 1]

Aim: Riemann Sums & Definite Integrals Course: Calculus Do Now: Aim: What are Riemann Sums? Approximate the area under the curve y = 4 โ€“ x 2 for [-1, 1]
4-3 DEFINITE INTEGRALS MS. BATTAGLIA โ€“ AP CALCULUS.

4-3 DEFINITE INTEGRALS MS. BATTAGLIA โ€“ AP CALCULUS.
If the partition is denoted by P, then the length of the longest subinterval is called the norm of P and is denoted by. As gets smaller, the approximation.

If the partition is denoted by P, then the length of the longest subinterval is called the norm of P and is denoted by. As gets smaller, the approximation.
1 Copyright ยฉ 2015, 2011 Pearson Education, Inc. Chapter 5 Integration.

1 Copyright ยฉ 2015, 2011 Pearson Education, Inc. Chapter 5 Integration.
4-3: Riemann Sums & Definite Integrals

4-3: Riemann Sums & Definite Integrals
Warm Up 1) 2) 3)Approximate the area under the curve for 0 < t < 40, given by the data, above using a lower Reimann sum with 4 equal subintervals. 4)Approximate.

Warm Up 1) 2) 3)Approximate the area under the curve for 0 < t < 40, given by the data, above using a lower Reimann sum with 4 equal subintervals. 4)Approximate.
1 Definite Integrals Section 4.3. 2 The Definite Integral The definite integral as the area of a region: If f is continuous and non-negative on the closed.

1 Definite Integrals Section The Definite Integral The definite integral as the area of a region: If f is continuous and non-negative on the closed.
Sigma Notations Example This tells us to start with k=1 This tells us to end with k=100 This tells us to add. Formula.

Sigma Notations Example This tells us to start with k=1 This tells us to end with k=100 This tells us to add. Formula.
Section 4.3 Day 1 Riemann Sums and Definite Integrals AP Calculus BC.

Section 4.3 Day 1 Riemann Sums and Definite Integrals AP Calculus BC.
Lesson 5-2 The Definite Integral. Ice Breaker See handout questions 1 and 2.

Lesson 5-2 The Definite Integral. Ice Breaker See handout questions 1 and 2.
5.2 Definite Integrals Objectives SWBAT: 1) express the area under a curve as a definite integral and as a limit of Riemann sums 2) compute the area under.

5.2 Definite Integrals Objectives SWBAT: 1) express the area under a curve as a definite integral and as a limit of Riemann sums 2) compute the area under.
Chapter 6 Integration Section 5 The Fundamental Theorem of Calculus (Day 1)

Chapter 6 Integration Section 5 The Fundamental Theorem of Calculus (Day 1)
4.3 Riemann Sums and Definite Integrals Definition of the Definite Integral If f is defined on the closed interval [a, b] and the limit of a Riemann sum.

4.3 Riemann Sums and Definite Integrals Definition of the Definite Integral If f is defined on the closed interval [a, b] and the limit of a Riemann sum.
Riemann sums & definite integrals (4.3) January 28th, 2015.

Riemann sums & definite integrals (4.3) January 28th, 2015.
CHAPTER 2 2.4 Continuity Fundamental Theorem of Calculus In this lecture you will learn the most important relation between derivatives and areas (definite.

CHAPTER Continuity Fundamental Theorem of Calculus In this lecture you will learn the most important relation between derivatives and areas (definite.
Riemann Sum. Formula Step 1 Step 2 Step 3 Riemann Sum.

Riemann Sum. Formula Step 1 Step 2 Step 3 Riemann Sum.
Section 4.3 Day 2 Riemann Sums & Definite Integrals AP Calculus BC.

Section 4.3 Day 2 Riemann Sums & Definite Integrals AP Calculus BC.
Definite Integrals. Definite Integral is known as a definite integral. It is evaluated using the following formula Otherwise known as the Fundamental.

Definite Integrals. Definite Integral is known as a definite integral. It is evaluated using the following formula Otherwise known as the Fundamental.
4.3 Finding Area Under A Curve Using Area Formulas Objective: Understand Riemann sums, evaluate a definite integral using limits and evaluate using properties.

4.3 Finding Area Under A Curve Using Area Formulas Objective: Understand Riemann sums, evaluate a definite integral using limits and evaluate using properties.

Similar presentations

Ads by Google