What is the integral from 1 to 0 of 1/x ?

The integral from 1 to 0 of 1/x is diverges

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integral from 1 to 0 of 1/x

\int_{1}^{0} \frac{1}{x} d x

diverges

Solution steps

\int_{1}^{0} \frac{1}{x} d x

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{0}^{1} \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= - [ln ∣ x ∣]_{0}^{1}

Compute the boundaries:

diverges

= diverges

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

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\int_{- 1}^{0} - x^{2} d x

\int_{1}^{e} x d x

\int_{- 2}^{2} (- 2 x^{2} + 8) d x

What is the integral from 1 to 0 of 1/x ?
The integral from 1 to 0 of 1/x is diverges