integral from-pi to 0 of-x^2-pix

解答

\int_{- π}^{0} - x^{2} - π x d x

\frac{π ^{3}}{6}

十进制

5.16771 \dots

求解步骤

\int_{- π}^{0} - x^{2} - π x d x

使用积分加法定则:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - \int_{- π}^{0} x^{2} d x - \int_{- π}^{0} π x d x

\int_{- π}^{0} x^{2} d x = \frac{π ^{3}}{3}

\int_{- π}^{0} π x d x = - \frac{π ^{3}}{2}

= - \frac{π ^{3}}{3} - (- \frac{π ^{3}}{2})

化简

- \frac{π ^{3}}{3} - (- \frac{π ^{3}}{2}) : \frac{π ^{3}}{6}

= \frac{π ^{3}}{6}

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