>>12945836Essentially, we calculate the area under the curve over a fixed interval by taking the antiderivative and calculating the difference between the two end-points. It's nonsensical to plug indeterminates into this. To get around this, we calculate the integral over some arbitrary finite interval and calculate the limit as this interval becomes arbitrarily large.
Now that limits are coming into play we need to be considerate of the hierarchy of limits. For example, diverges faster than . Why is this important? Well depending on how we define our arbitrary interval, we may obtain radically different solutions. If we take the integral over the interval and calculate the limit as n approaches infinity, this will yield a different result than calculating the integral over the interval and taking that limit.
Well, if the problem arises from defining our arbitrary interval, is there a canonical interval? Well, the answer is no.
