What is the integral from pi/6 to pi/2 of cot^2(x) ?

The integral from pi/6 to pi/2 of cot^2(x) is -pi/3+sqrt(3)

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integral from pi/6 to pi/2 of cot^2(x)

\int_{\frac{π}{6}}^{\frac{π}{2}} cot^{2} (x) d x

- \frac{π}{3} + 3

Decimal Notation

0.68485 \dots

Solution steps

\int_{\frac{π}{6}}^{\frac{π}{2}} cot^{2} (x) d x

Rewrite using trig identities

= \int_{\frac{π}{6}}^{\frac{π}{2}} - 1 + csc^{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}{6}}^{\frac{π}{2}} 1 d x + \int_{\frac{π}{6}}^{\frac{π}{2}} csc^{2} (x) d x

\int_{\frac{π}{6}}^{\frac{π}{2}} 1 d x = \frac{π}{3}

\int_{\frac{π}{6}}^{\frac{π}{2}} csc^{2} (x) d x = 3

= - \frac{π}{3} + 3

\int_{0}^{π} π - x d x

\int_{0}^{8} x^{2} - 6 x + 5 d x

\int_{- 1}^{2} x^{3} - x^{2} - 2 x d x

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

\int_{0}^{y} (x + y)^{2} d x

What is the integral from pi/6 to pi/2 of cot^2(x) ?
The integral from pi/6 to pi/2 of cot^2(x) is -pi/3+sqrt(3)