improper or proper intergral[1,4] tan(t - 1)dt

[kpx001]

intergral[1,4] tan(t - 1)dt
how would i solve to see if this is proper or not? i know that tan dne when cos = 0 but i dunno how to solve this with trig? change it to sin(t-1)/cos(t-1) . i know that inside 1,4 is pi/2 which makes it 0 but is there an algebraic way to solve this? thanks

 

[tkhunny]

You don't SOLVE anything to see if it is PROPER or IMPROPER.

Since you already split out the cosine, perhaps that's the easiest place to start.

For t in [1-4], we have (t-1) in [0,3].

For (t-1) in [0,3], we have cos(t-1) = 0 for t-1 = pi/2. There's your problem, right there.

It's improper.

Did you really want to know if it converges?