integral from pi to 3 of csc^2(θ)

解答

\int_{π}^{3} csc^{2} (θ) d θ

发散

求解步骤

\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

使用积分常见定则:

\int csc^{2} (θ) d θ = - cot (θ)

= - [- cot (θ)]_{3}^{π}

带入上下限计算后得:

发散

= 发散

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