What is the integral from 1 to 2 of (2x^{-2}-3) ?

The integral from 1 to 2 of (2x^{-2}-3) is -2

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integral from 1 to 2 of (2x^{-2}-3)

\int_{1}^{2} (2 x^{- 2} - 3) d x

- 2

Solution steps

\int_{1}^{2} 2 x^{- 2} - 3 d x

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

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

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

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

= 1 - 3

Simplify

= - 2

What is the integral from 1 to 2 of (2x^{-2}-3) ?
The integral from 1 to 2 of (2x^{-2}-3) is -2