integral from-1 to 4 of 3x^2+8x-5

解答

\int_{- 1}^{4} 3 x^{2} + 8 x - 5 d x

100

求解步骤

\int_{- 1}^{4} 3 x^{2} + 8 x - 5 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_{- 1}^{4} 3 x^{2} d x + \int_{- 1}^{4} 8 x d x - \int_{- 1}^{4} 5 d x

\int_{- 1}^{4} 3 x^{2} d x = 65

\int_{- 1}^{4} 8 x d x = 60

\int_{- 1}^{4} 5 d x = 25

= 65 + 60 - 25

化简

= 100

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

\int \frac{7 - 5 x}{64 - 49 x ^{2}} d x

\int \frac{( 2 x - 3 )}{x ^{2} + 6 x + 4} d x

f (x) = e^{x} + e^{- x}

t \to 0 lim (\frac{1 - cos ( t )}{t})