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

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

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

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

- \frac{π}{4} + 1

Decimal

0.21460 \dots

Solution steps

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

Rewrite using trig identities

= \int_{\frac{π}{4}}^{\frac{π}{2}} - 1 + csc^{2} (θ) d θ

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - \int_{\frac{π}{4}}^{\frac{π}{2}} 1 d θ + \int_{\frac{π}{4}}^{\frac{π}{2}} csc^{2} (θ) d θ

\int_{\frac{π}{4}}^{\frac{π}{2}} 1 d θ = \frac{π}{4}

\int_{\frac{π}{4}}^{\frac{π}{2}} csc^{2} (θ) d θ = 1

= - \frac{π}{4} + 1

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