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Today's calculation of Integral 732

Source: 2011 Hokkaido University entrance exam/Medicine etc.

July 3, 2011
calculusintegrationparameterizationtrigonometrycalculus computations

Problem Statement

Let aa be parameter such that 0<a<2π0<a<2\pi. For 0<x<2π0<x<2\pi, find the extremum of F(x)=∫xx+a1−cos⁡θ dθF(x)=\int_{x}^{x+a} \sqrt{1-\cos \theta}\ d\theta.
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