What is the integral from 0 to pi of (sec(x))^2 ?

The integral from 0 to pi of (sec(x))^2 is diverges

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integral from 0 to pi of (sec(x))^2

\int_{0}^{π} (sec (x))^{2} d x

diverges

Solution steps

\int_{0}^{π} (sec (x))^{2} d x

Take the denominator(s) of

(sec (x))^{2}

and compare to zero:

x = \frac{π}{2}

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_{0}^{\frac{π}{2}} (sec (x))^{2} d x + \int_{\frac{π}{2}}^{π} (sec (x))^{2} d x

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

diverges

If part of the expression diverges, then entire expression diverges

= diverges

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What is the integral from 0 to pi of (sec(x))^2 ?
The integral from 0 to pi of (sec(x))^2 is diverges