What is the integral from 0 to pi/2 of tan^2(θ) ?

The integral from 0 to pi/2 of tan^2(θ) is diverges

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integral from 0 to pi/2 of tan^2(θ)

\int_{0}^{\frac{π}{2}} tan^{2} (θ) d θ

diverges

Solution steps

\int_{0}^{\frac{π}{2}} tan^{2} (θ) d θ

Rewrite using trig identities

= \int_{0}^{\frac{π}{2}} - 1 + sec^{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_{0}^{\frac{π}{2}} 1 d θ + \int_{0}^{\frac{π}{2}} sec^{2} (θ) d θ

\int_{0}^{\frac{π}{2}} 1 d θ = \frac{π}{2}

\int_{0}^{\frac{π}{2}} sec^{2} (θ) d θ =

diverges

If part of the expression diverges, then entire expression diverges

= diverges

\int_{1}^{4} 5 d x

\int_{1}^{4} 2 d x

\int_{0}^{\frac{1}{2}} x d x

\int_{1}^{4} 2 x + 1 d x

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

What is the integral from 0 to pi/2 of tan^2(θ) ?
The integral from 0 to pi/2 of tan^2(θ) is diverges