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**Mrs. Cartledge Arc length**

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

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Objectives Determine the length of a curve.

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**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.

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**Sum of Disks as the Volume (revisited)**

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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.

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**The length of one segment**

P5 P4

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**The length of all segments**

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**Definition of Arc Length**

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**Example Applying the Definition**

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Example Find the length of the specified curve. =

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**Algorithm to Find Arc Length**

Determine whether the length is with respect to x or y, and then find the endpoints for the interval. Find y’(x) or x’(y). Plug the derivative into the formula: Evaluate.

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

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

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

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Sample Find the length of the specified curve. y = (x2 – 4)2 [0, 4 ]

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**Example A Vertical Tangent**

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Sample y = x1/5 [-1,4]

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Closure Explain the difference in these two formulas.

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**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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Riemann Sums and Definite Integration y = 6 y = x ex: Estimate the area under the curve y = x 2 + 2 from x = 0 to 3 using 3 subintervals and right endpoints,

Riemann Sums and Definite Integration y = 6 y = x ex: Estimate the area under the curve y = x 2 + 2 from x = 0 to 3 using 3 subintervals and right endpoints,

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