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

解答

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

\frac{134}{3}

十进制

44.66666 \dots

求解步骤

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

\int_{3}^{5} x^{2} d x = \frac{98}{3}

\int_{3}^{5} 2 x d x = 16

\int_{3}^{5} 2 d x = 4

= \frac{98}{3} + 16 - 4

化简

\frac{98}{3} + 16 - 4 : \frac{134}{3}

= \frac{134}{3}

\int_{0}^{1.1} sin (x^{2}) d x

\int_{0}^{x} \frac{sin ( y )}{y} d y

\int_{0}^{\frac{π}{2}} sin (sin (x)) d x

\int_{0}^{1} \frac{4}{3} (1 - x^{3}) d x

\int_{0}^{2 π} (sin (3 x))^{2} d x