What is the integral from pi/6 to pi/3 of csc^2(θ) ?

The integral from pi/6 to pi/3 of csc^2(θ) is -1/(sqrt(3))+sqrt(3)

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integral from pi/6 to pi/3 of csc^2(θ)

\int_{\frac{π}{6}}^{\frac{π}{3}} csc^{2} (θ) d θ

- \frac{1}{3} + 3

Decimal Notation

1.15470 \dots

Solution steps

\int_{\frac{π}{6}}^{\frac{π}{3}} csc^{2} (θ) d θ

Use the common integral:

\int csc^{2} (θ) d θ = - cot (θ)

= [- cot (θ)]_{\frac{π}{6}}^{\frac{π}{3}}

Compute the boundaries:

- \frac{1}{3} + 3

= - \frac{1}{3} + 3

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

\int_{0}^{\frac{1}{2}} 2 x e^{- x^{2}} d x

\int_{0}^{3} 4 x e^{- x} d x

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

\int_{\frac{1}{2}}^{\frac{e}{2}} x ln (2 x) d x

What is the integral from pi/6 to pi/3 of csc^2(θ) ?
The integral from pi/6 to pi/3 of csc^2(θ) is -1/(sqrt(3))+sqrt(3)