integral from-1 to 1 of k(3-x^2)

解答

\int_{- 1}^{1} k (3 - x^{2}) d x

\frac{16}{3} k

求解步骤

\int_{- 1}^{1} k (3 - x^{2}) d x

提出常数:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= k \cdot \int_{- 1}^{1} 3 - x^{2} 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

= k (\int_{- 1}^{1} 3 d x - \int_{- 1}^{1} x^{2} d x)

\int_{- 1}^{1} 3 d x = 6

\int_{- 1}^{1} x^{2} d x = \frac{2}{3}

= k (6 - \frac{2}{3})

化简

6 - \frac{2}{3} : \frac{16}{3}

= \frac{16}{3} k

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