Deelles said: Equation's wrong, if F'(x)=f(x), ∫f(x)dx would be =F(x), not F(x)+C (unless C equals zero), and the integral doesn't even have integration variables.
Deelles said: Equation's wrong, if F'(x)=f(x), ∫f(x)dx would be =F(x), not F(x)+C (unless C equals zero), and the integral doesn't even have integration variables.
Yeah, I'm bored.
ARRRGGGHHH!! I FINALLY ESCAPE FROM THAT HELL YET YOU'RE TRYING TO DRAG ME BACK IN! How can you be so cruel?! DAMN FUNCTIONS! GET OUT OF MY LIFE YOU MONSTERS!!
Deelles said: Equation's wrong, if F'(x)=f(x), ∫f(x)dx would be =F(x), not F(x)+C (unless C equals zero), and the integral doesn't even have integration variables.
Keo said: ARRRGGGHHH!! I FINALLY ESCAPE FROM THAT HELL YET YOU'RE TRYING TO DRAG ME BACK IN! How can you be so cruel?! DAMN FUNCTIONS! GET OUT OF MY LIFE YOU MONSTERS!!
Don't say that, next semester is my turn to suffer Calculus ),:
Keo said: ARRRGGGHHH!! I FINALLY ESCAPE FROM THAT HELL YET YOU'RE TRYING TO DRAG ME BACK IN! How can you be so cruel?! DAMN FUNCTIONS! GET OUT OF MY LIFE YOU MONSTERS!!
Rather be doing regular functions than Taylor Series. Or triple integrals. Oh, and surface integrals.
No, when it's explicitly stated that f'(x) = F(x), then you don't need to include the constant of integration when integrating f'(x), because it is already encompassed within "F(x)". Adding the constant of integration would be adding a + 0, which is meaningless in this case.
The fundamental theorem of calculus states that (∫f(x)dx)'=f(x), but this is not equivalent to ∫f'(x)dx=f(x), because f'(x) has infinitely many primitives. What can be said, however, is that ∫f'(x)dx=f(x) <=> (∫f'(x)dx)(0)=f(0).
Wait till they get to partial differential equations, where the question types can be divided into half a dozen categories and require guesses to solve. With infinite series.
It takes 2 pages of solution for a single line of question.
aoi-hoshi said: No, when it's explicitly stated that f'(x) = F(x), then you don't need to include the constant of integration when integrating f'(x), because it is already encompassed within "F(x)". Adding the constant of integration would be adding a + 0, which is meaningless in this case.
Don't you think it would make perfect sense if your prof wrote that thing on the blackboard? Not only helps teaching students, it may even prompt a couple of questions. And professors love questions, at least they all claim to.
Well, when f'(x)=F(x) is explicitly stated, then F(x) cannot have a constant. Could be a topic of discussion for students who are being introduced to the concepts of differentiation, I suppose, to aid in understanding.
Though the proof is cooler than saying "Just 'cuz", imo.
boomersooner said: Rather be doing regular functions than Taylor Series. Or triple integrals. Oh, and surface integrals.
Man, fu-UH-huck surface integrals. I mean, I have a good grasp of most of fundamental calculus (e.g. derivatives, anti-derivatives, series), but throw in some line or surface integrals and my goose is cooked.
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