Infinity in integration

Hello everyone, I hope you’re having a great day.

I wanted to ask about infinity. When do I know if the infinity will make the integral =0? Because all I understand if the number is trying to approach a 0 then we can make it a 0. I hope someone can clear my confusion about it. Like in this question how is it approaching 0?

By applying the common limit:

u -> -infinity (e^u) = 0

This is proven by applying the limit property

Lim_x -> -infinity (2x+3)
a=2 n=1
= -infinity

Therefore 1/2 * 0 = 0

The limit as x approaches zero would be negative infinity, since the graph goes down forever as you approach zero from either side: As a general rule, when you are taking a limit and the denominator equals zero, the limit will go to infinity or negative infinity.

Hope this helps. Sorry I did this on my phone.

By any chance are you a pure/applied mathematics student?

Thank you for your reply, unfortunately I haven’t been introduced to the limit properties or the common limit, so is there a good video that can summarize them so I can understand it. So when I see -infinity I will assume directly it’s equal to 0? yes, I’m studying pure math.

Its much easier to explain the concept with a graph. The aysmptore of the line would be going down the negative end of the y axis to zero infinately. Thats the best way to explain it.

Nice im away to start my 1st year in Applied Mathematics at University of Abedeen. I just finished my HNC in Electrical Engineering but fell in love with mathematics. I have experience withe intergral and differential calculus through Engineering Mathematics 2 which was my final unit therefore definate intergrals are fresh in my head.

Which uni are you at?

Hello everyone, I hope you’re having a great day.

I wanted to ask about infinity. When do I know if the infinity will make the integral =0? Because all I understand if the number is trying to approach a 0 then we can make it a 0. I hope someone can clear my confusion about it. Like in this question how is it approaching 0?