Question

what is the general anti derivative of f(x)=−12cos(x)−25sin(x)

Answer 1

Hello there Miss Stephanie c:
Do you remember your sine and cosine derivatives?

Answer 2

cosine is derivative of sine, yes?
So anti-derivative of cosine is sine.

Answer 3

I know this sounds so stupid but is this question just asking for the general formula in summation notation?

Answer 4

No.
`General solution` means that there will be an arbitrary constant tacked onto the end of the equation.

Answer 5

nevermind

Answer 6

so its asking then for something along the lines of an indefinite integral?

Answer 7

Recall that when you take the derivative of something like this:\[\Large\rm y=2x+3\]\[\Large\rm y'=2\]The 3 vanishes into thin air, yes?
So what if I asked you for the general anti-derivative of:\[\Large\rm y=2\]Well you might be inclined to say:\[\Large\rm y=2x\]But what about the 3??
Or what about some other constant value?

Answer 8

So our anti-derivative of the example is actually:\[\Large\rm y=2x+c\]

Answer 9

Yes, indefinite :)
I wasn't sure if you had been introduced to "integration" yet, so I didn't want to use that word hehe.

Answer 10

Woops I shouldn't had called the anti-derivative of y, y.
That was sloppy :3 No big deal though.

Answer 11

lol I knew where you were going with it, I just needed clarification on what the question was actually asking.

Answer 12

ah ok ^^ good

Answer 13

Thank you for your help!!!