Find the arc length of the curve y = - ln (cosx) for 0 <=x<=pi/4
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Originally Posted by harry Find the arc length of the curve y = - ln (cosx) for 0 <=x<=pi/4 The arc length is: s = integral(x=0 to pi/4) sqrt[1+(y'(x))^2] dx which in this case is: s = integral(x=0 to pi/4) sqrt[1+tan^2(x)] dx ...= integral(x=0 to pi/4) 1/cos(x) dx ...= ln[tan(pi/4+pi/8)] - ln[tan(pi/4)] ...= ln[tan(3 pi/8) / tan(pi/4)] ~= 0.8814 RonL
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