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

解答

\int_{- 2}^{2} π (4 - x^{2}) d x

π \frac{32}{3}

十进制

33.51032 \dots

求解步骤

\int_{- 2}^{2} π (4 - x^{2}) d x

提出常数:

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

= π \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

= π (\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}

= π (16 - \frac{16}{3})

化简

16 - \frac{16}{3} : \frac{32}{3}

= π \frac{32}{3}

(y + 4) \cdot y^{^{'}} = 2 x y + 4 y, y (2) = 1

x \to + 9 - lim (\frac{- 7}{( x + 9 )})

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