What is the integral from pi/3 to pi/2 of csc(x) ?

The integral from pi/3 to pi/2 of csc(x) is 1/2 ln(3)

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integral from pi/3 to pi/2 of csc(x)

\int_{\frac{π}{3}}^{\frac{π}{2}} csc (x) d x

\frac{1}{2} ln (3)

Decimal Notation

0.54930 \dots

Solution steps

\int_{\frac{π}{3}}^{\frac{π}{2}} csc (x) d x

Apply u-substitution

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= [ln ∣ u ∣]_{\frac{3}{3}}^{1}

\frac{3}{3} = \frac{1}{3}

= [ln ∣ u ∣]_{\frac{1}{3}}^{1}

Compute the boundaries:

\frac{1}{2} ln (3)

= \frac{1}{2} ln (3)

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What is the integral from pi/3 to pi/2 of csc(x) ?
The integral from pi/3 to pi/2 of csc(x) is 1/2 ln(3)