A quick question on the integration

[saman]

Hi,
I just cannot find any proof for the following:

Lets assume we have two functions f(x) and r(x) and we know that at point t=t1 both functions are equal (t=t1 is the intersection point of the two functions) i.e. f(t1)=g(t1). Now if we get the integral of these two function can we also assume that the anti-derivative of the two functions are equal as well? can we assume F(t1)=G(t1)? and substitute F(t1) by G(t1)?

Thanks for your help

 

[HallsofIvy]

Hi,
I just cannot find any proof for the following:

Lets assume we have two functions f(x) and r(x) and we know that at point t=t1 both functions are equal (t=t1 is the intersection point of the two functions) i.e. f(t1)=g(t1). Now if we get the integral of these two function can we also assume that the anti-derivative of the two functions are equal as well? can we assume F(t1)=G(t1)? and substitute F(t1) by G(t1)?

Thanks for your help

I'm not sure exactly what you mean by this. There is no such thing as "the" anti-derivative. If F(t) is an anti-derivative for f, then so is F(t)+ C for any constant, C. Similarly, if G(t) is an anti-derivative for g then so is G(t)+ D for any constant D. For any functions, f and g, whether f(t1)= g(t1) or not, we can always choose the constants so they are equal at any given point.