What is the integral from 0 to pi of csc(x) ?

The integral from 0 to pi of csc(x) is diverges

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integral from 0 to pi of csc(x)

\int_{0}^{π} csc (x) d x

diverges

Solution steps

\int_{0}^{π} csc (x) d x

Rewrite using trig identities

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

Apply Integration By Parts

: [\frac{x - sin ( x ) \cdot \int - x cot ( x ) csc ( x ) d x}{sin ( x )}]_{0}^{π}

= [\frac{x - sin ( x ) \cdot \int - x cot ( x ) csc ( x ) d x}{sin ( x )}]_{0}^{π}

\int - x cot (x) csc (x) d x = x csc (x) - ln tan (\frac{x}{2})

= [\frac{x - sin ( x ) ( x csc ( x ) - ln tan ( \frac{x}{2} ) )}{sin ( x )}]_{0}^{π}

Compute the boundaries:

diverges

= diverges

\int_{\frac{π}{2}}^{π} 2 sin (x) d x

\int_{0}^{1} (x^{2} - 4 x + 4) d x

\int_{0}^{u} 11 + 12 t^{2} d t

\int_{4}^{5} x^{2} - 4 x d x

\int_{0}^{9} (x - \frac{1}{2}) d x

What is the integral from 0 to pi of csc(x) ?
The integral from 0 to pi of csc(x) is diverges