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 11/6

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

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

\frac{11}{6}

Decimal

1.83333 \dots

Solution steps

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

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

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

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

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

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

Simplify

\frac{7}{3} - \frac{1}{2} : \frac{11}{6}

= \frac{11}{6}

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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 11/6