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Calculating Arc Length of Curves: Examples and Integral Setup

This guide explores methods for calculating the length of curves defined by functions on a given interval. We present two examples: First, we find the arc length of the curve ( y = x^3 ) between the points (1, 1) and (4, 8). Second, we calculate the arc length of the curve ( x = y^2 ) from (0, 0) to (1, 1). Additionally, we set up the integral for the arc length of the hyperbola ( xy = 1 ) from point (1, 1) to (2, ½). Use these examples and your calculator to compute the arc lengths.

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Calculating Arc Length of Curves: Examples and Integral Setup

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  1. 8.1 Arc Length

  2. Arc Length: if f is continuous on [a, b], then the length of the curve y = f(x) , a ≤ x ≤ b, is

  3. Ex 1: Find the length of the arc of the curve, y2 = x3 between the points (1, 1) and (4, 8).

  4. Ex 2: Find the length of the arc of the curve, x = y2between the points (0, 0) and (1, 1).

  5. Arc Length Function:

  6. 3

  7. 8.1 pg. 546#1, 3, 5 – 17 EOO, 19, 21

  8. Ex 3: Set up the integral for the length of the arc of the hyperbola xy = 1 from the point (1, 1) to (2, ½). Use your calculator to evaluate. 4

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