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Today's calculation of Integral 431

Source: 2009 The University of Electro-Communications entrance exam

February 27, 2009
calculusintegrationfunctiontrigonometrycalculus computations

Problem Statement

Consider the function f(\theta) \equal{} \int_0^1 |\sqrt {1 \minus{} x^2} \minus{} \sin \theta|dx in the interval of 0≤θ≤π2 0\leq \theta \leq \frac {\pi}{2}. (1) Find the maximum and minimum values of f(θ) f(\theta). (2) Evaluate ∫0π2f(θ) dθ \int_0^{\frac {\pi}{2}} f(\theta)\ d\theta.
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