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

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

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integral from 2pi to 0 of tan(x)

\int_{2 π}^{0} tan (x) d x

diverges

Solution steps

\int_{2 π}^{0} tan (x) d x

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{0}^{2 π} tan (x) d x

Take the denominator(s) of

tan (x)

and compare to zero:

x = \frac{π}{2}, x = \frac{3 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}} tan (x) d x + \int_{\frac{π}{2}}^{\frac{3 π}{2}} tan (x) d x + \int_{\frac{3 π}{2}}^{2 π} tan (x) d x)

\int_{0}^{\frac{π}{2}} tan (x) d x =

diverges

If part of the expression diverges, then entire expression diverges

= diverges

\int_{0}^{π} cos^{2} (3 x) d x

\int_{0}^{4} e^{x^{2}} d x

\int_{x^{4}}^{0} cos (t^{2}) d t

\int_{- 2}^{0} x d x

\int_{5}^{\infty} \frac{1}{x} d x

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