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

解答

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

15

求解步骤

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

\int_{- 1}^{2} 3 x^{2} d x = 9

\int_{- 1}^{2} 4 x d x = 6

= 9 + 6

化简

= 15

\int - 4 x + 12 d x

y^{^{'}} = y^{2} x^{3}

a re a 3 x^{2} + 12, 4 x + 4, [- 3, 3]

d er i v a t i v e \frac{1}{1 + x + x ^{2} + x ^{3}}

\frac{d}{d x} (\frac{18}{( 1 + 3 x ) ^{3}})