ja

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

人気のある微分積分 >

integral from 0 to 4 of 6e^{2t}

解

\int_{0}^{4} 6 e^{2 t} d t

解

3 (e^{8} - 1)

+1

十進法表記

8939.87396 \dots

解答ステップ

\int_{0}^{4} 6 e^{2 t} d t

定数を除く:

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

= 6 \cdot \int_{0}^{4} e^{2 t} d t

u置換積分法を適用する

= 6 \cdot \int_{0}^{8} e^{u} \frac{1}{2} d u

定数を除く:

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

= 6 \cdot \frac{1}{2} \cdot \int_{0}^{8} e^{u} d u

共通積分を使用する:

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

= 6 \cdot \frac{1}{2} [e^{u}]_{0}^{8}

簡素化

6 \cdot \frac{1}{2} [e^{u}]_{0}^{8} : 3 [e^{u}]_{0}^{8}

= 3 [e^{u}]_{0}^{8}

限度を計算する:

e^{8} - 1

= 3 (e^{8} - 1)

グラフ

人気の例

integral from 1 to t of 2/(x^2+4x+3)

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

integral from 0 to x of 0.25e^{-0.25t}

\int_{0}^{x} 0.25 e^{- 0.25 t} d t

integral from 0 to 7 of sin(8x^2)

\int_{0}^{7} sin (8 x^{2}) d x

integral from 1 to 5 of x^2+x+2

\int_{1}^{5} x^{2} + x + 2 d x

integral from 1 to 4 of 4/(1-3x)

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