MathDB

620

Part of 2010 Today's Calculation Of Integral

Problems(1)

Today's calculation of Interal 620

Source:

7/1/2010
Let a, ba,\ b be real numbers. Suppose that a function f(x)f(x) satisfies f(x)=asin⁡x+bcos⁡x+∫−ππf(t)cos⁡t dtf(x)=a\sin x+b\cos x+\int_{-\pi}^{\pi} f(t)\cos t\ dt and has the maximum value 2π2\pi for −π≤x≤π-\pi \leq x\leq \pi. Find the minimum value of ∫−ππ{f(x)}2dx.\int_{-\pi}^{\pi} \{f(x)\}^2dx.
2010 Chiba University entrance exam
calculusintegrationfunctiontrigonometryconicsparabolacalculus computations