What is the integral from pi/8 to pi of 2sec^2(2θ) ?

The integral from pi/8 to pi of 2sec^2(2θ) is diverges

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integral from pi/8 to pi of 2sec^2(2θ)

\int_{\frac{π}{8}}^{π} 2 sec^{2} (2 θ) d θ

diverges

Solution steps

\int_{\frac{π}{8}}^{π} 2 sec^{2} (2 θ) d θ

Take the denominator(s) of

2 sec^{2} (2 θ)

and compare to zero:

θ = \frac{π}{4}, θ = \frac{3 π}{4}

If exist

b, a < b < c, f (b) =

undefined

, \int_{a}^{c} f (x) d x = \int_{a}^{b} f (x) d x + \int_{b}^{c} f (x) d x

= \int_{\frac{π}{8}}^{\frac{π}{4}} 2 sec^{2} (2 θ) d θ + \int_{\frac{π}{4}}^{\frac{3 π}{4}} 2 sec^{2} (2 θ) d θ + \int_{\frac{3 π}{4}}^{π} 2 sec^{2} (2 θ) d θ

\int_{\frac{π}{8}}^{\frac{π}{4}} 2 sec^{2} (2 θ) d θ =

diverges

If part of the expression diverges, then entire expression diverges

= diverges

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What is the integral from pi/8 to pi of 2sec^2(2θ) ?
The integral from pi/8 to pi of 2sec^2(2θ) is diverges