What is the integral from pi/4 to pi/3 of csc^2(θ) ?

The integral from pi/4 to pi/3 of csc^2(θ) is -1/(sqrt(3))+1

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integral from pi/4 to pi/3 of csc^2(θ)

\int_{\frac{π}{4}}^{\frac{π}{3}} csc^{2} (θ) d θ

- \frac{1}{3} + 1

Decimal

0.42264 \dots

Solution steps

\int_{\frac{π}{4}}^{\frac{π}{3}} csc^{2} (θ) d θ

Use the common integral:

\int csc^{2} (θ) d θ = - cot (θ)

= [- cot (θ)]_{\frac{π}{4}}^{\frac{π}{3}}

Compute the boundaries:

- \frac{1}{3} + 1

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

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What is the integral from pi/4 to pi/3 of csc^2(θ) ?
The integral from pi/4 to pi/3 of csc^2(θ) is -1/(sqrt(3))+1