integral from-1 to 6 of [5y-(y^2-6)]

解答

\int_{- 1}^{6} [5 y - (y^{2} - 6)] d y

\frac{343}{6}

十进制

57.16666 \dots

求解步骤

\int_{- 1}^{6} 5 y - (y^{2} - 6) d y

化简

= \int_{- 1}^{6} 5 y - y^{2} + 6 d y

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_{- 1}^{6} 5 y d y - \int_{- 1}^{6} y^{2} d y + \int_{- 1}^{6} 6 d y

\int_{- 1}^{6} 5 y d y = \frac{175}{2}

\int_{- 1}^{6} y^{2} d y = \frac{217}{3}

\int_{- 1}^{6} 6 d y = 42

= \frac{175}{2} - \frac{217}{3} + 42

化简

\frac{175}{2} - \frac{217}{3} + 42 : \frac{343}{6}

= \frac{343}{6}

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