integral from 3 to 7 of ((2x-3))/6

解答

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

\frac{14}{3}

十进制

4.66666 \dots

求解步骤

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

提出常数:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{6} \cdot \int_{3}^{7} 2 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

= \frac{1}{6} (\int_{3}^{7} 2 x d x - \int_{3}^{7} 3 d x)

\int_{3}^{7} 2 x d x = 40

\int_{3}^{7} 3 d x = 12

= \frac{1}{6} (40 - 12)

化简

\frac{1}{6} (40 - 12) : \frac{14}{3}

= \frac{14}{3}

\int \frac{x + 6}{5 - 4 x - x ^{2}} d x

\frac{d}{d t} (ln (cos (\frac{π}{2} - \frac{t}{2})))

\int (x + 2) e^{4 - 3 x} d x

n = 1 \sum \infty \frac{3 ^{n}}{n}

l a pl a ce t r an s f or m (t - 1) cos (4 (t - 1))