Section 7.4: Arc Length. Arc Length The arch length s of the graph of f(x) over [a,b] is simply the length of the curve.

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Presentation transcript:

Section 7.4: Arc Length

Arc Length The arch length s of the graph of f(x) over [a,b] is simply the length of the curve.

White Board Challenge Find the arch length s of the graph of f(x) = -3x + 12 over [1,3]. No Calculator

Linear Arc Length Find the arch length s of the graph of f(x) = mx + b over [a,b].

Arc Length as a Riemann Sum Find the arch length s of the graph of f(x) over [a,b]. Approximate the arch length with chords

Arc Length Formula Assume that f '(x) exists and is continuous on [a,b]. Then the arc length s of y = f (x) over [a,b] is equal to:

Example 1 Find the arc length s of the graph f (x) = 1/12 x 3 + x -1 over [1,3]. Find the derivative: Use the formula: The derivative is not defined at 0 but 0 is not in our interval. Thus we can use the arc length formula.

Example 2 Find the arc length s of the graph y = x 1/3 over [-8,8]. Find the derivative: Use the formula: The derivative is not defined at 0 and 0 is in our interval. Thus we can not use the arc length formula. Instead, try solving for x : Find the new derivative: Now the derivative is defined everywhere. Find the new limits: Right now, we can NOT evaluate this integral without a calculator.

White Board Challenge Find the arc length of the curve of y = x 2 – 4│x│ – x over [-4,4]. Calculator