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Today's calculation of Integral 619

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July 1, 2010
calculusintegrationfunctiontrigonometrylogarithmscalculus computations

Problem Statement

Consider a function f(x)=sin⁡x9+16sin⁡2x (0≤x≤π2).f(x)=\frac{\sin x}{9+16\sin ^ 2 x}\ \left(0\leq x\leq \frac{\pi}{2}\right). Let aa be the value of xx for which f(x)f(x) is maximized.
Evaluate ∫aπ2f(x) dx.\int_a^{\frac{\pi}{2}} f(x)\ dx.
2010 Saitama University entrance exam/Mathematics
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