integral from-2 to 4 of (-x^2+2x+8)

解答

\int_{- 2}^{4} (- x^{2} + 2 x + 8) d x

36

求解步骤

\int_{- 2}^{4} - x^{2} + 2 x + 8 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_{- 2}^{4} x^{2} d x + \int_{- 2}^{4} 2 x d x + \int_{- 2}^{4} 8 d x

\int_{- 2}^{4} x^{2} d x = 24

\int_{- 2}^{4} 2 x d x = 12

\int_{- 2}^{4} 8 d x = 48

= - 24 + 12 + 48

化简

= 36

\frac{d y}{d x} = (sin^{2} (2 x)) (cos^{2} (y))

t \frac{d y}{d t} = t^{3} + 20 t^{3} y

\int 1.5 sin (- x + 2) d x

d er i v a t i v e y = cos (x) - x sin (x)

f (x) = x^{\frac{1}{6}}