What is the integral from 3 to 8 of (7/(x^2)-1) ?

The integral from 3 to 8 of (7/(x^2)-1) is -85/24

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integral from 3 to 8 of (7/(x^2)-1)

\int_{3}^{8} (\frac{7}{x ^{2}} - 1) d x

- \frac{85}{24}

Decimal

- 3.54166 \dots

Solution steps

\int_{3}^{8} \frac{7}{x ^{2}} - 1 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_{3}^{8} \frac{7}{x ^{2}} d x - \int_{3}^{8} 1 d x

\int_{3}^{8} \frac{7}{x ^{2}} d x = \frac{35}{24}

\int_{3}^{8} 1 d x = 5

= \frac{35}{24} - 5

Simplify

\frac{35}{24} - 5 : - \frac{85}{24}

= - \frac{85}{24}

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What is the integral from 3 to 8 of (7/(x^2)-1) ?
The integral from 3 to 8 of (7/(x^2)-1) is -85/24