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_{0}^{\infty} x e^{- \frac{x}{5}} d x

\int_{0}^{3} 9 \cdot (9 - y^{2})^{\frac{1}{2}} d y

\int_{0}^{x^{2} + y^{2}} 1 d z

\int_{4}^{5} 3 x x^{2} - 16 d x

\int_{2}^{3} \frac{7}{1 + x ^{2}} 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