integral from-4 to-3 of x^2-(2x+15)

解答

\int_{- 4}^{- 3} x^{2} - (2 x + 15) d x

\frac{13}{3}

十进制

4.33333 \dots

求解步骤

\int_{- 4}^{- 3} x^{2} - (2 x + 15) d x

化简

= \int_{- 4}^{- 3} x^{2} - 2 x - 15 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_{- 4}^{- 3} x^{2} d x - \int_{- 4}^{- 3} 2 x d x - \int_{- 4}^{- 3} 15 d x

\int_{- 4}^{- 3} x^{2} d x = \frac{37}{3}

\int_{- 4}^{- 3} 2 x d x = - 7

\int_{- 4}^{- 3} 15 d x = 15

= \frac{37}{3} - (- 7) - 15

化简

\frac{37}{3} - (- 7) - 15 : \frac{13}{3}

= \frac{13}{3}

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