What is the integral from 1 to 3 of csc^2(3t) ?

The integral from 1 to 3 of csc^2(3t) is diverges

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integral from 1 to 3 of csc^2(3t)

\int_{1}^{3} csc^{2} (3 t) d t

diverges

Solution steps

\int_{1}^{3} csc^{2} (3 t) d t

Take the denominator(s) of

csc^{2} (3 t)

and compare to zero:

t = \frac{π}{3}, t = \frac{2 π}{3}

If exist

b, a < b < c, f (b) =

undefined

, \int_{a}^{c} f (x) d x = \int_{a}^{b} f (x) d x + \int_{b}^{c} f (x) d x

= \int_{1}^{\frac{π}{3}} csc^{2} (3 t) d t + \int_{\frac{π}{3}}^{\frac{2 π}{3}} csc^{2} (3 t) d t + \int_{\frac{2 π}{3}}^{3} csc^{2} (3 t) d t

\int_{1}^{\frac{π}{3}} csc^{2} (3 t) d t =

diverges

If part of the expression diverges, then entire expression diverges

= diverges

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What is the integral from 1 to 3 of csc^2(3t) ?
The integral from 1 to 3 of csc^2(3t) is diverges