integral from-2 to 2 of 4(4-x^2)

解答

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

\frac{128}{3}

十进制

42.66666 \dots

求解步骤

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

提出常数:

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

= 4 \cdot \int_{- 2}^{2} 4 - 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

= 4 (\int_{- 2}^{2} 4 d x - \int_{- 2}^{2} x^{2} d x)

\int_{- 2}^{2} 4 d x = 16

\int_{- 2}^{2} x^{2} d x = \frac{16}{3}

= 4 (16 - \frac{16}{3})

化简

4 (16 - \frac{16}{3}) : \frac{128}{3}

= \frac{128}{3}

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