How to determine all values of p for which the integral is improper. integral dx/(x^2+2) -3 to p ?????????

Question

How to determine all values of p for which the integral is improper.     integral dx/(x^2+2)   -3 to p   ?????????

anonymous · Answer

is the integral (1/(x^2 +2))dx ?

anonymous · Answer

true     from -3 to p

anonymous · Answer

and im assuming as p approaches infinity?

anonymous · Answer

okay lets get on ahead with this you might be confused how do you even integrate this? or do you have any clue

lgbasallote · Answer

$$\int_{-3}^p \frac{dx}{x^2 +2}dx$$

anonymous · Answer

i assumed  p approaches -infinite and +infinite~   i got   -pi/2   and pi/2

lgbasallote · Answer

lol too many dx

anonymous · Answer

what was your integration?

anonymous · Answer

$$\lim_{t \rightarrow p}$$$$[\tan^{-1} (x/\sqrt{2})]_{-3}^{t}$$

anonymous · Answer

alright perfect good job first we will say as tan^(-1)(infinity) = pi/2 and tan^(-1)(- infinity) = -pi/2 so now let us see as p approaches infinity we have

lim p --> inf = tan^(-1)( inf)/sqrt2 and  therefore this is simply pi/2/sqrt 2 = pi/2sqrt2 and as 
lim p --> -inf = tan^(-1)( -inf)/sqrt2 and this is simply -pi/2/sqrt2 = -pi/2sqrt2 :)

hope you followed

anonymous · Answer

thx buddy~ got it~