What is the integral from pi/4 to pi/2 of cot(y) ?

The integral from pi/4 to pi/2 of cot(y) is 1/2 ln(2)

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integral from pi/4 to pi/2 of cot(y)

\int_{\frac{π}{4}}^{\frac{π}{2}} cot (y) d y

\frac{1}{2} ln (2)

Decimal

0.34657 \dots

Solution steps

\int_{\frac{π}{4}}^{\frac{π}{2}} cot (y) d y

Rewrite using trig identities

= \int_{\frac{π}{4}}^{\frac{π}{2}} \frac{cos ( y )}{sin ( y )} d y

Apply u-substitution

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= [ln ∣ u ∣]_{\frac{2}{2}}^{1}

\frac{2}{2} = \frac{1}{2}

= [ln ∣ u ∣]_{\frac{1}{2}}^{1}

Compute the boundaries:

\frac{1}{2} ln (2)

= \frac{1}{2} ln (2)

What is the integral from pi/4 to pi/2 of cot(y) ?
The integral from pi/4 to pi/2 of cot(y) is 1/2 ln(2)