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

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

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

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

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

Decimal

0.34657 \dots

Solution steps

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

Rewrite using trig identities

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

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)

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

\int_{0}^{x} \frac{t}{t ^{2} + 1} d t

\int_{2}^{8} \frac{1}{x} d x

\int_{0}^{1} x^{6} d x

\int_{0}^{2 π} - sin^{2} (t) d t

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