Lecture 4 arc length
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Lecture 4 – Arc Length . Estimate the length of the given through appropriate choices for lower and upper bounds. Arc Length – curve has a certain length. 4. 4. 3. 3. 2. 2. 1. 1. Lengths (in general). Consider one segment out of n pieces and then let n go to i nfinity. f(x).

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Lecture 4 – Arc Length

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Lecture 4 arc length

Lecture 4 – Arc Length

Estimate the length of the given through appropriate choices for lower and upper bounds.

Arc Length – curve has a certain length

4

4

3

3

2

2

1

1


Lengths in general

Lengths (in general)

Consider one segment out of n pieces and then let n go to infinity.

f(x)

Use more and more hypotenuse lengths to better the approximations.

x


Example 1

Example 1

4

Find the length of the given curve.

3

2

1


Example 2

Example 2

f(x)

Find the length of the given curve.

1

x

1

2


Example 3

Example 3

Find the length of the given curve.

2

f(x)

1

x


Example 3 continued

Example 3 – continued

2

f(x)

1

x


Lecture 5 surface area

Lecture 5 – Surface Area

Find the surface area by revolving the curve around the y-axis.


Lecture 4 arc length

Find the surface area by revolving the curve around the x-axis.


Example 11

Example 1

Put the surface areas in decreasing order for the given curve.

A: revolved about the y-axis.

B: revolved about the x-axis.

C: revolved about the line x=2.


Example 1 continued

Example 1-continued

4

4

4

3

3

3

2

2

2

1

1

1


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