QuestionLet Determine the most general antiderivative of .
Studdy Solution
STEP 1
What is this asking?
We're looking for a function whose derivative is the constant function .
Watch out!
Don't forget to add the "*constant of integration*" at the end!
It's super important because there are infinitely many antiderivatives.
STEP 2
1. Find the antiderivative
2. Add the constant of integration
STEP 3
Alright, so we're given the function and we want to find its **antiderivative**.
In other words, we're looking for a function whose derivative is .
STEP 4
Think about it: the derivative of is .
Why? Because the **power rule** says that the derivative of (which is the same as ) is .
So, the derivative of is just times the derivative of , which is .
See? Perfect!
STEP 5
But wait!
There's more!
The derivative of a constant is always **zero**.
That means we could add *any* constant to and its derivative would still be .
STEP 6
For example, the derivative of is .
The derivative of is *also* .
Get it?
STEP 7
So, to capture *all* possible antiderivatives, we add a general constant, which we usually call "****".
STEP 8
The most general antiderivative of is , where is an arbitrary constant.
So, .
Was this helpful?