Integration between minus and positive infinity

[danhall]

I'm trying to understand some maths in a paper I'm reading. It states
"f(x) = integral_-∞^+∞ (hw) dx = 0, as h→0 at x = ±∞"
where h is height of an obstacle which is positive at small values of x and w is the vertical speed of a fluid.
I don't understand this statement. Why does the fact h tends towards 0 with large (positive and negative) values of x mean that integral_-∞^+∞ (h) dx = 0?

Can anyone help me to understand this?

Thanks

 

[Steven G]

I'm trying to understand some maths in a paper I'm reading. It states
"f(x) = integral_-∞^+∞ (hw) dx = 0, as h→0 at x = ±∞"
where h is height of an obstacle which is positive at small values of x and w is the vertical speed of a fluid.
I don't understand this statement. Why does the fact h tends towards 0 with large (positive and negative) values of x mean that integral_-∞^+∞ (h) dx = 0?

Can anyone help me to understand this?

Thanks

Why does the fact h tends towards 0 with large (positive and negative) values of x mean that integral_-∞^+∞ (h) dx = 0? This statement is simply not true. Suppose f(x) is always positive and close to 0 at extreme values then the integral (the area under the curve) would be positive. There is something which I feel that you are leaving out.