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

F ( x ) = 200 x + C F\left(x\right)=200x+C F ( x ) = 200 x + C

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

this problem, we're asked to find the antiderivative of the following function. Now recall that if we want to find the antiderivative of a function, what we need to do is think about what derivative would give us this function. Now you can see we just have the constant 200 here. And if I think about it, if I were to take the derivative of 200 x, that x would come off of the derivative, wouldn't take you the derivative, and give us just 200. So 200 x would be the antiderivative, and don't forget we have to add the constant of integration, c. So this right here would be the solution to this problem. Hope you found this video helpful.

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

F ( x ) = 200 x + C F\left(x\right)=200x+C F ( x ) = 200 x + C

F ( x ) = 0 F\left(x\right)=0 F ( x ) = 0

F ( x ) = 200 + C F\left(x\right)=200+C F ( x ) = 200 + C

F ( x ) = 200 x F\left(x\right)=200x F ( x ) = 200 x

7. Antiderivatives & Indefinite Integrals

Antiderivatives

Business Calculus

7. Antiderivatives & Indefinite Integrals

Antiderivatives

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Multiple Choice

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

$F\left(x\right)=0$

$F\left(x\right)=200+C$

$F\left(x\right)=200x$

$F\left(x\right)=200x+C$

Verified step by step guidance

Recognize that finding the antiderivative of a function involves reversing the process of differentiation. This means we are looking for a function F(x) such that F'(x) = f(x).

The given function is f(x) = 200. This is a constant function, and the antiderivative of a constant is the constant multiplied by x, plus an arbitrary constant of integration, C.

Using the antiderivative rule for constants, ∫a dx = ax + C, apply this to f(x) = 200. Here, a = 200.

The antiderivative of 200 is 200x. Don't forget to add the constant of integration, C, because the antiderivative is not unique without it.

Thus, the antiderivative of f(x) = 200 is F(x) = 200x + C.

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