What is the integral from pi/2 to pi of cot(x) ?

The integral from pi/2 to pi of cot(x) is diverges

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integral from pi/2 to pi of cot(x)

\int_{\frac{π}{2}}^{π} cot (x) d x

diverges

Solution steps

\int_{\frac{π}{2}}^{π} cot (x) d x

Rewrite using trig identities

= \int_{\frac{π}{2}}^{π} \frac{cos ( x )}{sin ( x )} d x

Apply u-substitution

: \int_{1}^{0} \frac{1}{u} d u

= \int_{1}^{0} \frac{1}{u} d u

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= - [ln ∣ u ∣]_{0}^{1}

Compute the boundaries:

diverges

= diverges

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\int_{- \infty}^{0} 7^{r} d r

What is the integral from pi/2 to pi of cot(x) ?
The integral from pi/2 to pi of cot(x) is diverges