MAT237Y1 Lecture Notes - Antiderivative, Classification Of Discontinuities, Power Rule
Document Summary
In 6. 1, we were basically calling the antiderivative a(x). Well, that was mostly to get you to see that it means the area function under the curve f(x). We usually denote the antiderivative of f(x) as f (x) (just like how we denoted the derivative of f(x) to be f(cid:48)(x)same thing). So, if f (x) is the antiderivative of f(x), then that means. 2 x2 is an antiderivative of f(x) = x. Take the derivative of f (cid:48)(x) to d dx. Notice how i said an antiderivative, not the antiderivative. Remember from 6. 1 how antiderivatives are not unique at all! There can be that constant at the end. I can"t stress it enough to remember that +c after each time you nd the antiderivative. Just like when we were dealing with derivatives, we created a symbol to mean take the derivative of this function and it was d for integrals (antiderivatives).
