What is the integral from pi/4 to pi/3 of cot(x) ?

The integral from pi/4 to pi/3 of cot(x) is (ln(3)-ln(2))/2

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integral from pi/4 to pi/3 of cot(x)

\int_{\frac{π}{4}}^{\frac{π}{3}} cot (x) d x

\frac{ln ( 3 ) - ln ( 2 )}{2}

Decimal Notation

0.20273 \dots

Solution steps

\int_{\frac{π}{4}}^{\frac{π}{3}} cot (x) d x

Rewrite using trig identities

= \int_{\frac{π}{4}}^{\frac{π}{3}} \frac{cos ( x )}{sin ( x )} d x

Apply u-substitution

: \int_{\frac{2}{2}}^{\frac{3}{2}} \frac{1}{u} d u

= \int_{\frac{2}{2}}^{\frac{3}{2}} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= [ln ∣ u ∣]_{\frac{2}{2}}^{\frac{3}{2}}

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

= [ln ∣ u ∣]_{\frac{1}{2}}^{\frac{3}{2}}

Compute the boundaries:

\frac{ln ( 3 ) - ln ( 2 )}{2}

= \frac{ln ( 3 ) - ln ( 2 )}{2}

\int x e^{- 7 x} d x

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x \to \infty lim (10 x)

\int 12 x ln (5 x) d x

What is the integral from pi/4 to pi/3 of cot(x) ?
The integral from pi/4 to pi/3 of cot(x) is (ln(3)-ln(2))/2