What is the integral from 0 to 7 of tan(x) ?

The integral from 0 to 7 of tan(x) is diverges

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integral from 0 to 7 of tan(x)

\int_{0}^{7} tan (x) d x

diverges

Solution steps

\int_{0}^{7} 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}}^{7} 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_{- 1}^{2} (x - 1)^{2} d x

\int_{0}^{\frac{π}{2}} sin (x - y) d y

\int_{0}^{1} x^{9} e^{- x} d x

\int_{0}^{π} e^{- x} sin (x) d x

\int_{0}^{2} \frac{1}{( x - 1 ) ( x - 3 )} d x

What is the integral from 0 to 7 of tan(x) ?
The integral from 0 to 7 of tan(x) is diverges