What is the integral from 7 to 8 of (5/(x^2)-1) ?

The integral from 7 to 8 of (5/(x^2)-1) is -51/56

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integral from 7 to 8 of (5/(x^2)-1)

\int_{7}^{8} (\frac{5}{x ^{2}} - 1) d x

- \frac{51}{56}

Decimal

- 0.91071 \dots

Solution steps

\int_{7}^{8} \frac{5}{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_{7}^{8} \frac{5}{x ^{2}} d x - \int_{7}^{8} 1 d x

\int_{7}^{8} \frac{5}{x ^{2}} d x = \frac{5}{56}

\int_{7}^{8} 1 d x = 1

= \frac{5}{56} - 1

Simplify

\frac{5}{56} - 1 : - \frac{51}{56}

= - \frac{51}{56}

What is the integral from 7 to 8 of (5/(x^2)-1) ?
The integral from 7 to 8 of (5/(x^2)-1) is -51/56