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Today's calculation of integral 94

Source: 1979 Yokohama City University entrance exam/medical

January 26, 2006
calculusintegrationlimittrigonometrycalculus computations

Problem Statement

Let aa be real numbers.Find the following limit value. lim⁡T→∞1T∫0T(sin⁡x+sin⁡ax)2dx. \lim_{T\rightarrow \infty} \frac{1}{T} \int_0^T (\sin x+\sin ax)^2 dx.
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