integral from 2 to 7 of (3x^2-6x+5)

解答

\int_{2}^{7} (3 x^{2} - 6 x + 5) d x

225

求解步骤

\int_{2}^{7} 3 x^{2} - 6 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_{2}^{7} 3 x^{2} d x - \int_{2}^{7} 6 x d x + \int_{2}^{7} 5 d x

\int_{2}^{7} 3 x^{2} d x = 335

\int_{2}^{7} 6 x d x = 135

\int_{2}^{7} 5 d x = 25

= 335 - 135 + 25

化简

= 225

\int_{1}^{x} lo g_{\frac{1}{2}} (t) d t

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

\int_{2}^{\infty} \frac{5}{x ^{3}} d x

\int_{0}^{π} \frac{1}{1 + cos ^{2} ( x )} d x

\int_{- 2}^{0} - 2 d x