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

The integral from pi/4 to pi/2 of csc^2(x) is 1

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

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

1

Solution steps

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

Use the common integral:

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

= [- cot (x)]_{\frac{π}{4}}^{\frac{π}{2}}

Compute the boundaries:

1

= 1

\int_{- 3}^{- 1} (x^{2} + x + 6) d x

\int_{1}^{7} 7 x^{- 4} d x

\int_{0}^{1} 3^{x} d x

\int_{1}^{2} \frac{1}{2} d x

\int_{0}^{2} - x^{2} - 3 x d x

What is the integral from pi/4 to pi/2 of csc^2(x) ?
The integral from pi/4 to pi/2 of csc^2(x) is 1