What is the integral from 1 to 2 of x^2+x^{-2} ?

The integral from 1 to 2 of x^2+x^{-2} is 17/6

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from 1 to 2 of x^2+x^{-2}

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

\frac{17}{6}

Decimal

2.83333 \dots

Solution steps

\int_{1}^{2} x^{2} + 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_{1}^{2} x^{2} d x + \int_{1}^{2} x^{- 2} d x

\int_{1}^{2} x^{2} d x = \frac{7}{3}

\int_{1}^{2} x^{- 2} d x = \frac{1}{2}

= \frac{7}{3} + \frac{1}{2}

Simplify

\frac{7}{3} + \frac{1}{2} : \frac{17}{6}

= \frac{17}{6}

What is the integral from 1 to 2 of x^2+x^{-2} ?
The integral from 1 to 2 of x^2+x^{-2} is 17/6