Graphing and Limits for Improper Integrals

[Dan350]

Do you need to know how to graph in order to establish which limit of an improper integrals is going to infinity?? for example:

∫tan(3x)dx from 0 to ∏/6

The integral diverges,, but how do you figure which constant you should use
In this problem they put it as the limit a b aproaches ∏/6 form the left.
then they just simply integtrate

Thank you so much!

 

[hsetennis]

A full-out graph wouldn't be necessary, but knowledge of tan(x)'s behavior is useful. Plugging in the values should reveal that tan(pi/2) = 1/0 on the unit circle, this requiring an improper integral.