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Today's calculation of Integral 215

Source: Tokyo University of Agriculture and Technology entrance exam 2007

August 28, 2007
calculusintegrationfunctiontrigonometrycalculus computations

Problem Statement

For a∈R a\in\mathbb{R}, let M(a) M(a) be the maximum value of the function f(x)\equal{}\int_{0}^{\pi}\sin (x\minus{}t)\sin (2t\minus{}a)\ dt. Evaluate ∫0π2M(a)sin⁡(2a) da \int_{0}^{\frac{\pi}{2}}M(a)\sin (2a)\ da.
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