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Today's calculation of Integral 533

Source: 1992 Tokyo Denki University entrance exam/Engineering

January 21, 2010
calculusintegrationfunctiontrigonometryanalytic geometryparameterizationalgebra

Problem Statement

Let C C be the circle with radius 1 centered on the origin. Fix the endpoint of the string with length 2π 2\pi on the point A(1, 0) A(1,\ 0) and put the other end point P P on the point P0(1, 2π) P_0(1,\ 2\pi). From this situation, when we twist the string around C C by moving the point P P in anti clockwise with the string streched tightly, find the length of the curve that the point P P draws from sarting point P0 P_0 to reaching point A A.
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