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Understanding Arc Length of Non-Linear Functions Using the Pythagorean Theorem

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This section focuses on calculating the arc length of non-linear functions using the Pythagorean Theorem and calculus techniques. By letting the segments become infinitesimally small, we aim to approximate the curve accurately. The process involves integrating and differentiating simultaneously, emphasizing careful application of both methods. We will apply the arc length formula to specific functions, such as finding the length of the curve defined by y = x^(3/2) from x = 0 to x = 4, and explore other examples to solidify understanding.

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Understanding Arc Length of Non-Linear Functions Using the Pythagorean Theorem

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  1. Section 7-4 Arc Length

  2. Find Length of a non-linear Function DL Length = L a b

  3. Find Length of a non-linear Function Use the Pythagorean Theorem to find the length of each line segment To get a better approximation of the curve, let DL, Dx, Dy get infinitesimally small DL Add all the line segments to get the arc length

  4. Arc Length in terms of x Arc Length in terms of y You will be mixing Derivative and Integration! Be careful with the two techniques.

  5. First find the derivative: • Find the length of the curve y = x3/2 from x = 0 to x = 4 Plug the info into the correct Arc length formula

  6. 2) Find the length of the curve for

  7. Find the length of the curvefrom y = 1 to y = 2.

  8. Cont’d

  9. Homework Page 485 # 3-7

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