What is the integral from 7 to 10 of x/7-7/x ?

The integral from 7 to 10 of x/7-7/x is 51/14-7(ln(10)-ln(7))

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integral from 7 to 10 of x/7-7/x

\int_{7}^{10} \frac{x}{7} - \frac{7}{x} d x

\frac{51}{14} - 7 (ln (10) - ln (7))

Decimal

1.14613 \dots

Solution steps

\int_{7}^{10} \frac{x}{7} - \frac{7}{x} 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}^{10} \frac{x}{7} d x - \int_{7}^{10} \frac{7}{x} d x

\int_{7}^{10} \frac{x}{7} d x = \frac{51}{14}

\int_{7}^{10} \frac{7}{x} d x = 7 (ln (10) - ln (7))

= \frac{51}{14} - 7 (ln (10) - ln (7))

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What is the integral from 7 to 10 of x/7-7/x ?
The integral from 7 to 10 of x/7-7/x is 51/14-7(ln(10)-ln(7))