Fundamental Theorem of Calculus

[legacyofpiracy]

I was just going through my notes and I was wondering if anyone could clarify this for me: this is taken from a problem we did in class

       x^3
d/dx= S  (t^4)-6 dt 
       5

alright so i understand how the derivative would actually be the function so i just left out the whole ani-derivative step we did and skipped to

f'(x)=(((x^3)^4)-6)*3x^2

here is where i was getting confused, shouldnt I then subtract the function with the lower limit plugged in?

in other words have this instead :  ((((x^3)^4)-6)*3x^2)-(5^4)-6

because of the formula F(b)-F(a) ?

Perhaps I forgot to copy down the rest of the answer into my notes, but I wanted to clarify this

 

[royhaas]

Note that from \(\displaystyle F(b)-F(a)\), you have the derivative \(\displaystyle F'(b)b'-F'(a)a'\), using the chain rule. And the derivative of a constant is zero.

 

[legacyofpiracy]

OH! that was stupid of me, thank you! :roll: