What is the integral from pi/6 to pi/4 of csc^2(x) ?

The integral from pi/6 to pi/4 of csc^2(x) is -1+sqrt(3)

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integral from pi/6 to pi/4 of csc^2(x)

\int_{\frac{π}{6}}^{\frac{π}{4}} csc^{2} (x) d x

- 1 + 3

Decimal

0.73205 \dots

Solution steps

\int_{\frac{π}{6}}^{\frac{π}{4}} csc^{2} (x) d x

Use the common integral:

\int csc^{2} (x) d x = - cot (x)

= [- cot (x)]_{\frac{π}{6}}^{\frac{π}{4}}

Compute the boundaries:

- 1 + 3

= - 1 + 3

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What is the integral from pi/6 to pi/4 of csc^2(x) ?
The integral from pi/6 to pi/4 of csc^2(x) is -1+sqrt(3)