What is the integral from pi to 3 of csc^2(θ) ?

The integral from pi to 3 of csc^2(θ) is diverges

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integral from pi to 3 of csc^2(θ)

\int_{π}^{3} csc^{2} (θ) d θ

diverges

Solution steps

\int_{π}^{3} csc^{2} (θ) d θ

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{3}^{π} csc^{2} (θ) d θ

Use the common integral:

\int csc^{2} (θ) d θ = - cot (θ)

= - [- cot (θ)]_{3}^{π}

Compute the boundaries:

diverges

= diverges

\int_{3}^{\infty} \frac{4}{x ^{3}} d x

\int_{\frac{π}{4}}^{x} cos (2 t) d t

\int_{0}^{7 2^{\circ}} sin^{2} (θ) sin (2 θ) d θ

\int_{0}^{\frac{π}{2}} 3 sin (t) cos (t) d t

\int_{0}^{\frac{π}{4}} cos (x^{3}) d x

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