What is the integral from a to 2a of (a-(a^3)/(x^2)) ?

The integral from a to 2a of (a-(a^3)/(x^2)) is a^2-(a^2)/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from a to 2a of (a-(a^3)/(x^2))

\int_{a}^{2 a} (a - \frac{a ^{3}}{x ^{2}}) d x

a^{2} - \frac{a ^{2}}{2}

Solution steps

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{a}^{2 a} a d x - \int_{a}^{2 a} \frac{a ^{3}}{x ^{2}} d x

\int_{a}^{2 a} a d x = a^{2}

\int_{a}^{2 a} \frac{a ^{3}}{x ^{2}} d x = \frac{a ^{2}}{2}

= a^{2} - \frac{a ^{2}}{2}

\frac{d}{d x} (\frac{2}{x ^{2} + 5})

\int cos (x) cos (sin (x)) d x

x \to + 5 - lim (\frac{5}{( x - 5 ) ^{3}})

\int \frac{( 3 x + 5 ) ^{3}}{10} d x

\frac{d}{d u} (u^{3} - 5 u^{2} + \frac{7}{3 u ^{2}} + 6)

What is the integral from a to 2a of (a-(a^3)/(x^2)) ?
The integral from a to 2a of (a-(a^3)/(x^2)) is a^2-(a^2)/2