Calculate the average value of on the interval .

MATHEMATICS · Single correct · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

Calculate the average value of f(x)=x2sin⁡xf(x)=x^{2}\sin x on the interval [−π,π][-\pi,\pi]. (a) π−4π\displaystyle \pi-\frac{4}{\pi} (b) π23\displaystyle \frac{\pi^{2}}{3} (c) 0 (d) π2−2π\displaystyle \frac{\pi}{2}-\frac{2}{\pi}

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