Finding the area under the curve y = 15x^(-0.5) from x = 0 to x = infinity

[EmmettC]

I have an equation of a negative power function form:

y = 15x^-0.5

Question 1: How can I calculate the area under the curve from x = 0 to x = infinity?
Question 2: Is there a meaningful inflection point for this equation? How would I interpret it--as the value of X where 50% of the area is to the left (i.e., approaching 0 on the x-axis), and 50% to the right of it (i.e., approaching infinity on x axis)?

Sorry if this is confusingly written. Thank you.

 

[tkhunny]

If you REALLY want it AT x = 0, you probably should pick a function that exists at x = 0.

On the other hand, it doesn't really need to exist, it just needs to converge. Since you have two directions that are not obvious, you should test them each for convergence.

Somewhat loosely, evaluate \(\displaystyle \displaystyle\int\limits_{a}^{b}\dfrac{15}{\sqrt{x}}\;dx\), and test the two desired directions separately.