integral from 0 to-1 of x

解答

\int_{0}^{- 1} x d x

\frac{1}{2}

十进制

0.5

求解步骤

\int_{0}^{- 1} x d x

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{- 1}^{0} x d x

使用幂法则

= - [\frac{x ^{2}}{2}]_{- 1}^{0}

带入上下限计算后得:

- \frac{1}{2}

= - (- \frac{1}{2})

化简

= \frac{1}{2}

\int_{1}^{2} ((2 - t) t) d t

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