AP Calculus BC

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A curtate cycloid is defined by the equations x = 2t - sin t and y = t - cos t. If I walk along the cycloid, how far will I walk in 10 seconds?

  • AP Calculus BC -

    ds^2 = dx^2+dy^2
    = (2-cos t)^2 + (1+sin t)^2
    = 4 - 4cost + cos^2 t + 1 + 2sint + sin^2 t
    = 6 - 4cost + 2sint

    The problem is, that this results in an elliptic integral, which is not usual in low-level calculus classes

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