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

解答

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

\frac{5}{6}

十进制

0.83333 \dots

求解步骤

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

\int_{2}^{3} x^{2} d x = \frac{19}{3}

\int_{2}^{3} 3 x d x = \frac{15}{2}

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

= \frac{19}{3} - \frac{15}{2} + 2

化简

\frac{19}{3} - \frac{15}{2} + 2 : \frac{5}{6}

= \frac{5}{6}

\int_{0}^{5} 15 x x + 4 d x

\int_{0}^{310} x^{2} d x

\int_{- 1}^{1} (- 30 x^{2} + 4 x y) d y

\int_{0}^{5} t^{2} + 2 t - 15 d t

\int_{0}^{2} \frac{1}{( 2 - x ) ^{\frac{5}{2}}} d x