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 v^1 to v^2 of 1/v

解

\int_{v^{1}}^{v^{2}} \frac{1}{v} d v

解

2 ln (v) - ln ∣ v ∣

解答ステップ

\int_{v^{1}}^{v^{2}} \frac{1}{v} d v

共通積分を使用する:

\int \frac{1}{v} d v = ln (∣ v ∣)

= [ln ∣ v ∣]_{v^{1}}^{v^{2}}

簡素化

= [ln ∣ v ∣]_{v}^{v^{2}}

限度を計算する:

2 ln (v) - ln ∣ v ∣

= 2 ln (v) - ln ∣ v ∣

人気の例

limit as x approaches-1 of 1/(x^2-1)

x \to - 1 lim (\frac{1}{x ^{2} - 1})

(d^2)/(dx^2)(9xsin(x^2))

\frac{d ^{2}}{d x ^{2}} (9 x sin (x^{2}))

(\partial)/(\partial x)(2x+1)

\frac{\partial}{\partial x} (2 x + 1)

(\partial)/(\partial z)(zcos(xz))

\frac{\partial}{\partial z} (z cos (x z))

integral from 1 to 2 of 2r^2ln(r)

\int_{1}^{2} 2 r^{2} ln (r) d r