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Section 9.1

Section 9.1. Arc Length. FINDING THE LENGTH OF A PLANE CURVE. Divide the interval [ a , b ] into n equal subintervals . Find the length of the straight line segments in each subinterval using the distance formula.

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Section 9.1

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  1. Section 9.1 Arc Length

  2. FINDING THE LENGTH OF A PLANE CURVE • Divide the interval [a, b] into n equal subintervals. • Find the length of the straight line segments in each subinterval using the distance formula. • Sum the lengths and take limit as the length of the subintervals go to zero. Compute definite integral.

  3. THE ARC LENGTH FORMULA The length of the curve y = f (x), a ≤ x ≤ b, where f ′ is continuous on [a, b], is

  4. ANOTHER ARC LENGTH FORMULA The length of the curve x = g(y), c ≤ y ≤ d, where g′ is continuous on [c, d], is

  5. THE ARC LENGTH FUNCTION Definition: Let C be a smooth curve with equation: y = f (x), a ≤ x ≤ b. The arc length function, s(x), the distance along the curve C from the initial point P0(a,f (a)) to the point Q(x, f (x)), is defined by

  6. THE DIFFERENTIAL OF ARC LENGTH The differential of the arc length is Thus, the arc length is the integral of the differential ds. L = ∫ ds

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