/sci/ - Science & Math

My dumb ass needs help with pic related, if somebody could point me in the right direction... so far I've got:

>g(x) is continuous, therefore integrable, therefore the RHS integral exists
>product of continuous functions is continuous, therefore the LHS integral exists
>in the special case where g(x)=0, both the LHS and RHS equal zero, so any value of c will do
>otherwise we can divide by the RHS integral to get some value k
>if k is within the range of f(x), the existence of c is implied by the Intermediate Value Theorem
>...
>I have no idea how to show this