integral from-3 to 3 of (sqrt(9-x^2))^2

解答

\int_{- 3}^{3} (9 - x^{2})^{2} d x

36

求解步骤

\int_{- 3}^{3} (9 - x^{2})^{2} d x

化简

(9 - x^{2})^{2} : 9 - x^{2}

= \int_{- 3}^{3} 9 - 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_{- 3}^{3} 9 d x - \int_{- 3}^{3} x^{2} d x

\int_{- 3}^{3} 9 d x = 54

\int_{- 3}^{3} x^{2} d x = 18

= 54 - 18

化简

= 36

\int e^{- 2 x} (x^{2} + 5) d x

t a y l or e^{x - 1}

\frac{d}{d x} (\frac{3 x y}{x ^{2} + y ^{2}})

y^{^{'''}} + 2 y^{^{''}} + y^{^{'}} + 2 y = 0

n \to \infty lim (n^{- 2})