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

解答

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

\frac{203}{6}

十进制

33.83333 \dots

求解步骤

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

\int_{- 2}^{5} x^{2} d x = \frac{133}{3}

\int_{- 2}^{5} 3 x d x = \frac{63}{2}

\int_{- 2}^{5} 3 d x = 21

= \frac{133}{3} - \frac{63}{2} + 21

化简

\frac{133}{3} - \frac{63}{2} + 21 : \frac{203}{6}

= \frac{203}{6}

\int_{- 3}^{0} \frac{1}{( x - 1 ) ^{2}} d x

\int_{- 6}^{3} - \frac{1}{x ^{4}} d x

\int_{0}^{2 π} 2 sin (θ) cos (θ) d θ

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

\int_{0}^{1} 8 t^{2} d t