integral from 6 to 7 of x^2-4x-12

解答

\int_{6}^{7} x^{2} - 4 x - 12 d x

\frac{13}{3}

十进制

4.33333 \dots

求解步骤

\int_{6}^{7} x^{2} - 4 x - 12 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_{6}^{7} x^{2} d x - \int_{6}^{7} 4 x d x - \int_{6}^{7} 12 d x

\int_{6}^{7} x^{2} d x = \frac{127}{3}

\int_{6}^{7} 4 x d x = 26

\int_{6}^{7} 12 d x = 12

= \frac{127}{3} - 26 - 12

化简

\frac{127}{3} - 26 - 12 : \frac{13}{3}

= \frac{13}{3}

\int_{1}^{\infty} \frac{1}{2 x + 7} d x

\int_{6}^{0} (2 + 5 x) e^{\frac{1}{3} x} d x

\int_{\frac{π}{2}}^{x} sin (7 t) d t

\int_{1}^{2} (3 x^{2} - 5 x + 2) d x

\int_{- \frac{π}{4}}^{\frac{π}{4}} 6 sec^{2} (x) d x