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

解答

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

100

求解步骤

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

\int_{- 1}^{3} 4 x^{3} d x = 80

\int_{- 1}^{3} 3 x^{2} d x = 28

\int_{- 1}^{3} 2 x d x = 8

= 80 + 28 - 8

化简

= 100

\int_{0}^{π} x sec^{2} (x) d x

\int_{- \infty}^{0} \frac{1}{5 x ^{3}} d x

\int_{0}^{\infty} 3 sin^{2} (a) d a

\int_{2}^{5} (\frac{5 x + 2}{3}) d x

\int_{a}^{b} \frac{1}{2} θ^{2} d θ