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人気のある微分積分 >

integral from 1 to 4 of-3e^{sqrt(x)}

解

\int_{1}^{4} - 3 e^{x} d x

解

- 6 e^{2}

+1

十進法表記

- 44.33433 \dots

解答ステップ

\int_{1}^{4} - 3 e^{x} d x

定数を除く:

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

= - 3 \cdot \int_{1}^{4} e^{x} d x

u置換積分法を適用する

= - 3 \cdot \int_{1}^{2} e^{u} \cdot 2 u d u

定数を除く:

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

= - 3 \cdot 2 \cdot \int_{1}^{2} e^{u} u d u

部分積分を適用する

= - 3 \cdot 2 [e^{u} u - \int e^{u} d u]_{1}^{2}

\int e^{u} d u = e^{u}

= - 3 \cdot 2 [e^{u} u - e^{u}]_{1}^{2}

簡素化

= - 6 [e^{u} u - e^{u}]_{1}^{2}

限度を計算する:

e^{2}

= - 6 e^{2}

グラフ

人気の例

integral of 20sec(4x)tan(4x)

\int 20 sec (4 x) tan (4 x) d x

integral of (3x^2)/(sqrt(25-x^2))

\int \frac{3 x ^{2}}{25 - x ^{2}} d x

limit as x approaches 7 of cos((pix)/3)

x \to 7 lim (cos (\frac{π x}{3}))

derivative y=sqrt(3x)

d er i v a t i v e y = 3 x

limit as x approaches 3 of 2x^3+4x-2

x \to 3 lim (2 x^{3} + 4 x - 2)