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Today's calculation of Integral 840

Source: 2012 Ehime University entrance exam/Science

August 2, 2012
calculusintegrationfunctiontrigonometryalgebradomaininequalities

Problem Statement

Let x, yx,\ y be real numbers. For a function f(t)=xsin⁡t+ycos⁡tf(t)=x\sin t+y\cos t, draw the domain of the points (x, y)(x,\ y) for which the following inequality holds. ∣∫−ππf(t)cos⁡t dt∣≤∫−ππ{f(t)}2dt.\left|\int_{-\pi}^{\pi} f(t)\cos t\ dt\right|\leq \int_{-\pi}^{\pi} \{f(t)\}^2dt.
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