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人気のある微分積分 >

integral from-1 to 0 of (xe^y-y)

解

\int_{- 1}^{0} (x e^{y} - y) d x

解

- y - \frac{1}{2} e^{y}

解答ステップ

\int_{- 1}^{0} x e^{y} - y d x

総和規則を適用する:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - \int_{- 1}^{0} y d x + \int_{- 1}^{0} e^{y} x d x

\int_{- 1}^{0} y d x = y

\int_{- 1}^{0} e^{y} x d x = - \frac{1}{2} e^{y}

= - y - \frac{1}{2} e^{y}

人気の例

integral from 1 to 5 of 5/2 e^{0.4x}

\int_{1}^{5} \frac{5}{2} e^{0.4 x} d x

integral from 0 to r of (br^3+cr^2)

\int_{0}^{r} (b r^{3} + c r^{2}) d r

integral from 1 to 5 of ((3x)/(x^3))

\int_{1}^{5} (\frac{3 x}{x ^{3}}) d x

integral from 0 to a of sin(x)

\int_{0}^{a} sin (x) d x

integral from-3 to 4 of x^2+3x+1

\int_{- 3}^{4} x^{2} + 3 x + 1 d x