net change

Question

the net change in y=f(x), as x changes from a to b is given by___________.

 

∫abs(F'(x)) dx

 

∫F'(x) dx

 

 ∫ abs(F(x)) dx

 

 ∫F(x) dx

 

 none of these

Answer 1

If F'(x) = f(x), the answer is none of these. The net change in f is f(b) - f(a)

Neither of the integrals involving the absolute value can be computed until you know the sign of F or F".

The integral of F'(x) = F(b) - F(a)l is the integral of f from a to b, not the change of f. The integral of F(x) from a to b is the integral of the integral of f, not the change of f.