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Today's caluculation of Integral 208

Source: Waseda University entrnace exam/Education 1979

May 31, 2007
calculusintegrationfunctiontrigonometrycalculus computations

Problem Statement

Find the values of real numbers a, ba,\ b for which the function f(x)=a∣cos⁡x∣+b∣sin⁡x∣f(x)=a|\cos x|+b|\sin x| has local minimum at x=−π3x=-\frac{\pi}{3} and satisfies ∫−π2π2{f(x)}2dx=2\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\{f(x)\}^{2}dx=2.
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