# Lecture 4 – Arc Length - PowerPoint PPT Presentation

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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

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 infinity.

f(x)

Use more and more hypotenuse lengths to better the approximations.

x

### Example 1

4

Find the length of the given curve.

3

2

1

### Example 2

f(x)

Find the length of the given curve.

1

x

1

2

### Example 3

Find the length of the given curve.

2

f(x)

1

x

2

f(x)

1

x

### Lecture 5 – Surface Area

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

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

### Example 1

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

C: revolved about the line x=2.

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4

4

3

3

3

2

2

2

1

1

1