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

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

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

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

π - \frac{π}{4} - 1

Decimal Notation

1.35619 \dots

Solution steps

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

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

\int_{\frac{π}{4}}^{\frac{π}{2}} 2 d x = π - \frac{π}{2}

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

= π - \frac{π}{2} - (- \frac{π}{4} + 1)

Simplify

π - \frac{π}{2} - (- \frac{π}{4} + 1) : π - \frac{π}{4} - 1

= π - \frac{π}{4} - 1

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