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Calculus Mrs. Cartledge Arc length Sec 7.4 Phantom’s Revenge Kennywood Park.

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Presentation on theme: "Calculus Mrs. Cartledge Arc length Sec 7.4 Phantom’s Revenge Kennywood Park."— Presentation transcript:

1 Calculus Mrs. Cartledge Arc length Sec 7.4 Phantom’s Revenge Kennywood Park

2 Objectives Determine the length of a curve.

3 Area Under a Curve (revisited) We use the definite integral to find the area under a curve. The limits of integration are a and b. The height of the rectangle is represented by f(x), the width by dx and the sum by the definite integral.

4 Sum of Disks as the Volume (revisited)

5 Finding Arc Length We want to determine the length of the continuous function f(x) on the interval [a,b]. Initially we’ll need to estimate the length of the curve. We’ll do this by dividing the interval up into n equal subintervals each of width  x and we’ll denote the point on the curve at each point by Pi. We can approximate the curve by a series of straight lines connecting the points.

6 The length of one segment P4P4 P5P5

7 The length of all segments

8 Definition of Arc Length

9 Example Applying the Definition

10 Example Find the length of the specified curve. =

11 Algorithm to Find Arc Length 1.Determine whether the length is with respect to x or y, and then find the endpoints for the interval. 2.Find y’(x) or x’(y). 3.Plug the derivative into the formula: 4.Evaluate.

12 Sample [1,2] Find the length of the specified curve.

13 Sample Find the length of the specified curve. You are given the x values but you need c and d!!

14 Sample Find the length of the specified curve. y = sin(x) [0, ¶ ]

15 Sample Find the length of the specified curve. y = (x 2 – 4) 2 [0, 4 ]

16 Example A Vertical Tangent

17 Sample y = x 1/5 [-1,4]

18 Closure Explain the difference in these two formulas.

19 Independent Assignment Notebook: p 485 # 3 - #11 odd. Check your answers in the back of the book. Graded Assignment: HW Sec 7.4 in Schoology. Enter the first ½ of the answers in Schoology. Due Tuesday, May 15, before class.


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