integral from 0 to 7 of 5/3 x

解答

\int_{0}^{7} \frac{5}{3} x d x

\frac{245}{6}

十进制

40.83333 \dots

求解步骤

\int_{0}^{7} \frac{5}{3} x d x

提出常数:

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

= \frac{5}{3} \cdot \int_{0}^{7} x d x

使用幂法则

= \frac{5}{3} [\frac{x ^{2}}{2}]_{0}^{7}

带入上下限计算后得:

\frac{49}{2}

= \frac{5}{3} \cdot \frac{49}{2}

化简

= \frac{245}{6}

in v erse l a pl a ce - \frac{1}{s ^{2} + ( 5 ) ^{2}}

\int_{- 3}^{0} 9 - x^{2} d x

in v erse l a pl a ce \frac{3 s - 1}{( s ^{2} + 2 s + 5 )}

\frac{d y}{d x} = 3 (y^{2} + 1), y (\frac{π}{4}) = 1

y^{^{'}} - y = 2 t e^{2 t}