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

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

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

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

1

Solution steps

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

Use the common integral:

\int csc^{2} (θ) d θ = - cot (θ)

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

Compute the boundaries:

1

= 1

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

\int_{0}^{\frac{1}{4}} \frac{3}{1 + 16 x ^{2}} d x

\int_{2}^{x} \frac{( 3 - x )}{2} d x

\int_{2}^{6} 5 d x

\int_{0}^{6} (x - 6)^{2} d x

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