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 1 of 2e^{x/3+4}

解

\int_{0}^{1} 2 e^{\frac{x}{3} + 4} d x

解

6 e^{4} (3 e - 1)

+1

十進法表記

129.59823 \dots

解答ステップ

\int_{0}^{1} 2 e^{\frac{x}{3} + 4} d x

定数を除く:

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

= 2 \cdot \int_{0}^{1} e^{\frac{x}{3} + 4} d x

e^{\frac{x}{3} + 4} = e^{4} e^{\frac{x}{3}}

= 2 \cdot \int_{0}^{1} e^{4} e^{\frac{x}{3}} d x

定数を除く:

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

= 2 e^{4} \cdot \int_{0}^{1} e^{\frac{x}{3}} d x

u置換積分法を適用する

= 2 e^{4} \cdot \int_{0}^{\frac{1}{3}} e^{u} \cdot 3 d u

定数を除く:

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

= 2 e^{4} \cdot 3 \cdot \int_{0}^{\frac{1}{3}} e^{u} d u

共通積分を使用する:

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

= 2 e^{4} \cdot 3 [e^{u}]_{0}^{\frac{1}{3}}

簡素化

= 6 e^{4} [e^{u}]_{0}^{\frac{1}{3}}

限度を計算する:

3 e - 1

= 6 e^{4} (3 e - 1)

グラフ

人気の例

integral from 1 to infinity of 6x^{-7}

\int_{1}^{\infty} 6 x^{- 7} d x

integral from 1 to 4 of f(x+5)

\int_{1}^{4} f (x + 5) d x

integral from 0 to 1 of 10x^4e^{x^5}

\int_{0}^{1} 10 x^{4} e^{x^{5}} d x

integral from 1 to e^3 of 1/x

\int_{1}^{e^{3}} \frac{1}{x} d x

integral from 0 to 4pi of 6+2cos(1/2 x)

\int_{0}^{4 π} 6 + 2 cos (\frac{1}{2} x) d x