If where f is a continuous function find f(4) and f'(4)
use Fundamental therom of Calculus
so I know that I'm going to let
and then differentiate both sides but how do i defferentiate
and it's derivate how do i do that
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Another question with this F.T.C stuff
Use F.T.C find a function and a number c such that
for x>0
So I know i gotta differentiate both sides but how would i find a number C when F.T.C would just eliminate it since derivative of a number is 0
Use F.T.C find a function and a number c such that
for x>0
So I know i gotta differentiate both sides but how would i find a number C when F.T.C would just eliminate it since derivative of a number is 0
derivative ...
go back to the original integral equation and sub in ...
Well, as , and as , so it makes sense that
Maple confirms that is the correct answer.
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However, that raises a question of my own: Where did I go wrong below:
Now we can take the limit as to get
I feel like I made a really fundamental error and am just not seeing it. I know that if , the limit is , so where is my reasoning faulty?
Hmm yes, I got this answer as well but however in the choices i have to pick from it's not there...
however -1/2 is so i convinced myself that maybe -infnity had something to do with it
oh btw, redsoxfan325 you are godlike math genius (:
could you help me out with this one as well:
I really don't know where to go with this I attempted to trigsubstiution but then that got really messy, I don't think parts will work, and I dont think theres anything i can normally substitute ):
First, the inverse sine integral should be found in any table of integrals. Second, break the integral up into two parts:
First integral:
Let . Thus
The integral is now
Second integral:
Thus,
So
Subtracting the first and second integrals gives
Sorry it took so long. That one was tough.
1.) (Good luck, it's a hard one!)
2.)
3.)
4.)
5.) (This is an easy u-substitution...if you know what to use for u!)
6.)
I think that's enough to keep you busy for a while, as most of these aren't easy.