- #1

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## Homework Statement

I have the following expression

$$I = \int_{-\infty}^{0} f_p(p) \ \big[ pf_x(a - \frac{p}{m}t) \big] dp + \int_{0}^{\infty} f_p(p) \ \big[ pf_x(a - \frac{p}{m}t) \big] dp$$

where ##f_p## and ##f_x## are normalised distributions. In particular, ##f_x## is symmetric about ##x=a##. This also means that ##pf_x(a - \frac{p}{m}t) ## is anti-symmetric about ##p = 0##.

Is there any way through which I can prove (or disprove) that ##I## is positive if

$$\int_{-\infty}^{0} f_p(p) dp < \int_{0}^{\infty} f_p(p) dp $$

ie the area under the graph on the -ve ##p##-axis is smaller than that on the +ve ##p##-axis?

Some guidance regarding how to start is greatly appreciated. Thanks in advance!