What is the integral from 0 to pi of tan(2t) ?

The integral from 0 to pi of tan(2t) is diverges

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integral from 0 to pi of tan(2t)

\int_{0}^{π} tan (2 t) d t

diverges

Solution steps

\int_{0}^{π} tan (2 t) d t

Take the denominator(s) of

tan (2 t)

and compare to zero:

t = \frac{π}{4}, t = \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_{0}^{\frac{π}{4}} tan (2 t) d t + \int_{\frac{π}{4}}^{\frac{3 π}{4}} tan (2 t) d t + \int_{\frac{3 π}{4}}^{π} tan (2 t) d t

\int_{0}^{\frac{π}{4}} tan (2 t) d t =

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 tan(2t) ?
The integral from 0 to pi of tan(2t) is diverges