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Arc Length and Surfaces of Revolution

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Presentation on theme: "Arc Length and Surfaces of Revolution"— Presentation transcript:

1 Arc Length and Surfaces of Revolution
Lesson 7.4 Arc Length and Surfaces of Revolution

2 We want to be able to find the distance travelled by an object along a curve
This is the same as finding the length of a curve from a given point to another The integral we will use comes from the infinite limit of the lengths of segments along the curve

3 Arc Length Along a Curve
Distance, s, is given by or If the function is differentiable along the interval [a, b]

4 Example Find the arc length on the interval [1, 2]

5 Area of a Surface of Revolution
We are trying to find the lateral area of the cylinder below: The formula for this is found using circumference and “length” of the cylinder circumference Cylinder length

6 The length, L, in this formula is the length of the curve used earlier
Then, applying an infinite limit of infinitely small cylinders along with a changing radius, we get the integral for surface area of revolution: If the length, L, of the cylinder is vertical then

7 Answer Example Find the surface area formed by revolving
around the x-axis from 1 to 4. Answer ~30.85

8 Answer Example Find the surface area formed by revolving
around the y-axis from 0 to 2. Answer ~36.18


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