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

= \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)

\int_{0}^{x} \frac{1}{3} d x

\int_{0}^{0.5} 2 x + 3 - x e^{3 x} d x

\int_{0}^{1} \frac{9}{1 + p ^{2}} d p

\int_{- 4}^{5} (25 - x^{2}) - (5 - x) d x

\int_{0}^{12} π (1 + \frac{x}{3})^{2} d x

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)