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Section 7.4: Arc Length

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

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Section 7.4: Arc Length

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  1. Section 7.4: Arc Length

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

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

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

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

  6. 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:

  7. Example 1 The derivative is not defined at 0 but 0 is not in our interval. Thus we canuse the arc length formula. Find the arc length s of the graph f (x) = 1/12 x3+ x-1over [1,3]. Find the derivative: Use the formula:

  8. Example 2 Find the arc length s of the graph y = x1/3over [-8,8]. The derivative is not defined at 0 and 0 is in our interval. Thus we can not use the arc length formula. Find the derivative: Instead, try solving for x: Now the derivative is defined everywhere. Find the new derivative: Right now, we can NOT evaluate this integral without a calculator. Find the new limits: Use the formula:

  9. White Board Challenge Calculator Find the arc length of the curve of y= x2 – 4│x│ – x over [-4,4].

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