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人気のある微分積分 >

integral from 1 to 3 of 0.2e^{0.2t}

解

\int_{1}^{3} 0.2 e^{0.2 t} d t

解

0.60071 \dots

解答ステップ

\int_{1}^{3} 0.2 e^{0.2 t} d t

定数を除く:

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

= 0.2 \cdot \int_{1}^{3} e^{0.2 t} d t

u置換積分法を適用する

= 0.2 \cdot \int_{0.2}^{0.6} e^{u} \frac{1}{0.2} d u

定数を除く:

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

= 0.2 \cdot \frac{1}{0.2} \cdot \int_{0.2}^{0.6} e^{u} d u

簡素化

= 0.2 \cdot 5 \cdot \int_{0.2}^{0.6} e^{u} d u

共通積分を使用する:

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

= 0.2 \cdot 5 [e^{u}]_{0.2}^{0.6}

簡素化

= [e^{u}]_{0.2}^{0.6}

限度を計算する:

0.60071 \dots

= 0.60071 \dots

グラフ

人気の例

integral from 2 to 3 of 2x-x^2

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

integral from 5 to 9 of (x-5)

\int_{5}^{9} (x - 5) d x

integral from 0 to t of (t-w)e^{7w}

\int_{0}^{t} (t - w) e^{7 w} d w

integral from 1 to 4 of (x+3)

\int_{1}^{4} (x + 3) d x

integral from-1 to 5 of (3-|x|)

\int_{- 1}^{5} (3 - ∣ x ∣) d x