integral from-10 to 10 of (x^2+x)

解答

\int_{- 10}^{10} (x^{2} + x) d x

\frac{2000}{3}

十进制

666.66666 \dots

求解步骤

\int_{- 10}^{10} x^{2} + 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_{- 10}^{10} x^{2} d x + \int_{- 10}^{10} x d x

\int_{- 10}^{10} x^{2} d x = \frac{2000}{3}

\int_{- 10}^{10} x d x = 0

= \frac{2000}{3} + 0

化简

= \frac{2000}{3}

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