integral from 4 to 5 of ((e^y)/3)^2

解答

\int_{4}^{5} (\frac{e ^{y}}{3})^{2} d y

\frac{e ^{10} - e ^{8}}{18}

十进制

1058.08376 \dots

求解步骤

\int_{4}^{5} (\frac{e ^{y}}{3})^{2} d y

使用分布积分法

= [\frac{1}{9} e^{2 y} y - \int \frac{2}{9} e^{2 y} y d y]_{4}^{5}

\int \frac{2}{9} e^{2 y} y d y = \frac{1}{18} (2 e^{2 y} y - e^{2 y})

= [\frac{1}{9} e^{2 y} y - \frac{1}{18} (2 e^{2 y} y - e^{2 y})]_{4}^{5}

化简

[\frac{1}{9} e^{2 y} y - \frac{1}{18} (2 e^{2 y} y - e^{2 y})]_{4}^{5} : [\frac{1}{18} e^{2 y}]_{4}^{5}

= [\frac{1}{18} e^{2 y}]_{4}^{5}

带入上下限计算后得:

\frac{e ^{10} - e ^{8}}{18}

= \frac{e ^{10} - e ^{8}}{18}

n = 1 \sum \infty \frac{n ^{4}}{2 ^{n}}

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

\int 10 sin (x) 2 x d x

d er i v a t i v e \frac{x}{x + 3}

y^{^{''}} - y = 0, y (0) = 1, y^{^{'}} (0) = 2