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

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

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integral from pi/3 to pi/2 of 1/(sin(x))

\int_{\frac{π}{3}}^{\frac{π}{2}} \frac{1}{sin ( x )} d x

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

Decimal

0.54930 \dots

Solution steps

\int_{\frac{π}{3}}^{\frac{π}{2}} \frac{1}{sin ( x )} d x

Apply u-substitution

= \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)

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