What is the integral from pi/6 to pi/2 of cot(x) ?

The integral from pi/6 to pi/2 of cot(x) is ln(2)

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integral from pi/6 to pi/2 of cot(x)

\int_{\frac{π}{6}}^{\frac{π}{2}} cot (x) d x

ln (2)

Decimal

0.69314 \dots

Solution steps

\int_{\frac{π}{6}}^{\frac{π}{2}} cot (x) d x

Rewrite using trig identities

= \int_{\frac{π}{6}}^{\frac{π}{2}} \frac{cos ( x )}{sin ( x )} d x

Apply u-substitution

= \int_{\frac{1}{2}}^{1} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= [ln ∣ u ∣]_{\frac{1}{2}}^{1}

Compute the boundaries:

ln (2)

= ln (2)

What is the integral from pi/6 to pi/2 of cot(x) ?
The integral from pi/6 to pi/2 of cot(x) is ln(2)