Find the antiderivative of the following function.
$f\left(x\right)=200$

• A. $F\left(x\right)=0$
• B. $F\left(x\right)=200+C$
• C. $F\left(x\right)=200x$
• D. $F\left(x\right)=200x+C$

Answer: (D)

Verified step by step guidance

1. Identify the function to be integrated: f(x) = 200.
2. Recall that the antiderivative of a constant 'a' is 'ax + C', where 'C' is the constant of integration.
3. Apply the antiderivative rule to the function f(x) = 200. The antiderivative will be 200x + C.
4. Understand that the constant 'C' represents an infinite number of possible vertical shifts of the antiderivative function.
5. Conclude that the antiderivative of f(x) = 200 is F(x) = 200x + C.