integral from-8 to 0 of (2+sqrt(64-x^2))

解答

\int_{- 8}^{0} (2 + 64 - x^{2}) d x

16 + 16 π

十进制

66.26548 \dots

求解步骤

\int_{- 8}^{0} 2 + 64 - 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

= \int_{- 8}^{0} 2 d x + \int_{- 8}^{0} 64 - x^{2} d x

\int_{- 8}^{0} 2 d x = 16

\int_{- 8}^{0} 64 - x^{2} d x = 16 π

= 16 + 16 π