What is the integral from 0 to pi/2 of pi/(sin(x)) ?

The integral from 0 to pi/2 of pi/(sin(x)) is diverges

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integral from 0 to pi/2 of pi/(sin(x))

\int_{0}^{\frac{π}{2}} \frac{π}{sin ( x )} d x

diverges

Solution steps

\int_{0}^{\frac{π}{2}} \frac{π}{sin ( x )} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= π \cdot \int_{0}^{\frac{π}{2}} \frac{1}{sin ( x )} d x

Apply u-substitution

= π \cdot \int_{0}^{1} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= π [ln ∣ u ∣]_{0}^{1}

Compute the boundaries:

diverges

= diverges

What is the integral from 0 to pi/2 of pi/(sin(x)) ?
The integral from 0 to pi/2 of pi/(sin(x)) is diverges