Section 9.1 Arc Length and Surface Area I

Slides:

Advertisements

Similar presentations

Section 5.3 – The Definite Integral

Advertisements

Section 5.3: Evaluating Definite Integrals Practice HW from Stewart Textbook (not to hand in) p. 374 # 1-27 odd, odd.

MAT 1235 Calculus II 4.1, 4.2 Part I The Definite Integral

A car accelerates from a stop to 45 m/sec in 4 sec. Explain why the car must have been accelerating at exactly m/sec at some moment. 2 Do Now.

MAT 1235 Calculus II 4.4 Part II Indefinite Integrals and the Net Change Theorem

MAT 3751 Analysis II 5.2 The Riemann Integral Part I

Section 7.4: Arc Length. Arc Length The arch length s of the graph of f(x) over [a,b] is simply the length of the curve.

MAT 1235 Calculus II Section 8.2 Area of a Surface of Revolution

MAT 1235 Calculus II Section 7.8 Improper Integrals I

Section 5.9 Approximate Integration Practice HW from Stewart Textbook (not to hand in) p. 421 # 3 – 15 odd.

Section 5.1/5.2: Areas and Distances – the Definite Integral Practice HW from Stewart Textbook (not to hand in) p. 352 # 3, 5, 9 p. 364 # 1, 3, 9-15 odd,

MAT 1235 Calculus II Section 6.5 Exponential Growth and Decay

MAT 3237 Differential Equations Section 2.2 Separable Equations

MAT 1234 Calculus I Section 2.3 Part II Differentiation Formulas

MAT 1234 Calculus I Section 1.6 Part II Using the Limit Laws

MAT 1235 Calculus II Section 5.1 Area Between Curves

Vector Valued Functions

Section 9.1 Arc Length. FINDING THE LENGTH OF A PLANE CURVE Divide the interval [a, b] into n equal subintervals. Find the length of the straight line.

7.4 Lengths of Curves Quick Review What you’ll learn about A Sine Wave Length of a Smooth Curve Vertical Tangents, Corners, and Cusps Essential Question.

Section 12.3 The Dot Product

MAT 1226 Calculus II Section 10.4 Areas and Length in Polar Coordinates

MAT 1235 Calculus II Section 9.1 Modeling with Differential Equations

Section 9.2 Area of a Surface of Revolution. THE AREA OF A FRUSTUM The area of the frustum of a cone is given by.

MAT 1228 Series and Differential Equations Section 4.1 Definition of the Laplace Transform

MAT 1235 Calculus II Section 7.5 Strategy For Integration

MAT 1236 Calculus III Section 10.2 Calculus with Parametric Curves

Riemann Sum. Formula Step 1 Step 2 Step 3 Riemann Sum.

Announcements Topics: -sections 7.3 (definite integrals), 7.4 (FTC), and 7.5 (additional techniques of integration) * Read these sections and study solved.

1. 課程大綱 OUTLINE Line Integrals （曲線積分） Surface Integral （曲面積分） 2.

MAT 1226 Calculus II Section 6.2* The Natural Logarithmic Function

MAT 1235 Calculus II 4.3 Part I The Fundamental Theorem of Calculus

MTH 252 Integral Calculus Chapter 6 – Integration Section 6.6 – The Fundamental Theorem of Calculus Copyright © 2005 by Ron Wallace, all rights reserved.

The Fundamental Theorem of Calculus is appropriately named because it establishes connection between the two branches of calculus: differential calculus.

Arc Length & Surfaces of Revolution (7.4)

Applied Calculus (MAT 121) Dr. Day Wednesday, March 28, 2012

Chapter 5 The Definite Integral. Chapter 5 The Definite Integral.

MAT 3237 Differential Equations

Section 10.1 Separable Equations I

Section 11.1 Sequences Part I

Calculus I (MAT 145) Dr. Day Monday November 27, 2017

Chapter 5 Integrals.

Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. {image}

Calculus II (MAT 146) Dr. Day Wednesday, February 28, 2018

Unit 6 – Fundamentals of Calculus Section 6

Arc Length and Surfaces of Revolution

Calculus II (MAT 146) Dr. Day Wednesday Jan 17, 2018

MAT 1236 Calculus III Section 11.7 Taylor Series

Section 4.2 Contour Integrals

MAT 3237 Series and Differential Equations

Section 2.6 Trigonometric Limits

Sec 5.3: THE FUNDAMENTAL THEOREM OF CALCULUS

Calculus II (MAT 146) Dr. Day Friday, February 23, 2018

Warm Up 1. Find 2 6 2

Section 15.1 Functions of Several variables

Section 10.4 Linear Equations

Chapter 6 Applications of Derivatives Section 6.2 Definite Integrals.

Warm Up 1. Find 2 6 2

Section 5.2 Definite Integrals

Section 5.3 – The Definite Integral

Section 5.3 – The Definite Integral

Calculus I (MAT 145) Dr. Day Wednesday April 17, 2019

Calculus II (MAT 146) Dr. Day Monday, February 26, 2018

Chapter 5 Integration.

5.5 Further Properties of the Riemann Integral II

Section 8.7 Improper Integrals I

5.7 Part I The Substitution Rule

Section 6.2* The Natural Logarithmic Function

Section 6.4* General Log. and Exponential Functions

Presentation transcript:

Section 9.1 Arc Length and Surface Area I MAT 1235 Calculus II Section 9.1 Arc Length and Surface Area I http://myhome.spu.edu/lauw

HW… WebAssign 9.1I

Preview Derive the formula for the length of a segment of a curve.

Arc Length

Riemann Sum, Definite Integral Any limit of the form : can be interpreted as

Quote... “Formula come, formula go – they’ll drift in and out of your life, almost like characters in a favorite book. When you finally close the cover, the characters have told their story and you start up again with another book, complete with new characters and adventures. Then you find yourself focusing on the new ones, not the ones from the past.”

Arc Length

Arc Length

Recall: The Mean Value Theorem Let 𝑓 be a function satisfies the following conditions: 1. 𝑓 is continuous on the closed interval [𝑎,𝑏]. 2. 𝑓 is differentiable on the open interval (𝑎,𝑏). Then there is a number 𝑐 in (𝑎,𝑏) such that or, equivalently,

The Mean Value Theorem a c b

Arc Length

Arc Length

Example 1 Find the length of the curve

Arc Length (second formula)

Bonus Problem You may get bonus points for submitting a type up solutions of this problem. Must be your own work, do not Google. There are at least 3 different solutions. Find the length of the curve

Classwork Work with your team partner only. Do not “announce” your answer/solution.