What is the integral from 100 to s of 1/(0.2s) ?

The integral from 100 to s of 1/(0.2s) is 5(ln|s|-2ln(10))

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integral from 100 to s of 1/(0.2s)

\int_{100}^{s} \frac{1}{0.2 s} d s

5 (ln ∣ s ∣ - 2 ln (10))

Solution steps

\int_{100}^{s} \frac{1}{0.2 s} d s

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{0.2} \cdot \int_{100}^{s} \frac{1}{s} d s

Simplify

= 5 \cdot \int_{100}^{s} \frac{1}{s} d s

Use the common integral:

\int \frac{1}{s} d s = ln (∣ s ∣)

= 5 [ln ∣ s ∣]_{100}^{s}

Compute the boundaries:

ln ∣ s ∣ - 2 ln (10)

= 5 (ln ∣ s ∣ - 2 ln (10))

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What is the integral from 100 to s of 1/(0.2s) ?
The integral from 100 to s of 1/(0.2s) is 5(ln|s|-2ln(10))