Improper Integrals

[w4taup]

Hey guys I just wanted to post a couple problems that I've been having trouble with. It's a new section that we've been learning but I don't quite understand how it works.

Explain why each of the following integrals is improper.

1a) x^4 e^-x^4 dx between infinity and 1

b) sec x dx between pie/2 and 0

c) 1/x^2 +5 between 0 and - infinity

Answers: a)Since there is an infinite interval of integration which is why it's an improper integral.

b) Since lim sec x=0. Thus given integral is improper due to infinite discontinuity.

c) Due to infinite intervals, the integral is improper.

I'm sorry if I'm not showing enough work but I just need to understand how and why these questions are what they are and why those answers apply to them. If anyone can help me out with this I'd really appreciate it. Sorry if it's asking too much, I've been trying to understand this for a while now and I need to know how

 

[tkhunny]

a) I do not know that the given explanation is sufficient. I think youalso need the non-zero argument throughout an infinite segment of the Domain.

b) sec(x) = 1/cos(x), cos(pi/2) = 0. sec(x) increases without bound around x = pi/2.

c) It's not particularly clear what is written. Did you forget your Order of Operations? Same arguemnt as a), anyway.