Question

an explanation please:

Answer 1

U(x)=−∫F(x)dx+C
find F(x). according to my book it should be done this way but I dont understand the logic behind it.
ddx∫F(x)dx=F(x)
F(x)=−dU(x)dx

Answer 2

original question: http://openstudy.com/users/bronzegoddess#/updates/51fad2f4e4b0259e2c33bd2b

Answer 3

think of it this way, the integral is the opposite of a derivative

so combining an integral with derivative with respect to the same variable will cancel each other out

Answer 4

what ended up happening for your problem is,
the derivative with respect to x was taken on both sides

then f(x) was solved

the constant "C" disappears because the derivative of a constant is zero

Answer 5

Given that U(x) = - ∫F(x)dx + C, then - U(x) = ∫F(x)dx + C [1] (the sign of C does not change, as C may be anything). The differential of an integral is equal to the function that was being integrated, but without any constant, as the differential of a constant is 0. So d/dx (∫F(x)dx + C) = F(x) [2]. Now substituting [1] into [2] gives F(x) = -dU(x)/dx.

Answer 6

thank you both, i wish i could give two medals but incognito was more specific :/

Answer 7

You're welcome :)