integral from-3 to 3 of (13-x^2)-(x^2-5)

解答

\int_{- 3}^{3} (13 - x^{2}) - (x^{2} - 5) d x

72

求解步骤

\int_{- 3}^{3} 13 - x^{2} - (x^{2} - 5) d x

化简

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

\int_{- 3}^{3} 2 x^{2} d x = 36

\int_{- 3}^{3} 18 d x = 108

= - 36 + 108

化简

= 72

\int \frac{1}{x ^{2} + 169} d x

(2 x + 1) (\frac{d y}{d x}) + y = (2 x + 1)^{\frac{3}{2}}

y^{^{''}} + 3 y = - 48 x^{2} e^{3 x}

f (x) = arcsinh (x)

\int - 510 x^{2} + 3414 x + 1998 d x