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I'm trying to figure out if this is true - any help would be greatly appreciated!

If a(x) < b(x) between the values x_i and x_f then is the following also true?...

int_{x_i}^{x_f} dx f(x) a(x) < int_{x_i}^{x_f} dx f(x) b(x)

where f(x)>0 for all x.

...I think it is true, but I'd like to be able to prove it!

Thanks,

Jenny