What is the antiderivative of 5?
Understand the Problem
The question is asking for the antiderivative of the constant 5. This involves finding a function whose derivative equals 5. The high-level approach involves applying the rule for finding antiderivatives of constant functions.
Answer
$5x + C$
Answer for screen readers
The antiderivative of 5 is $5x + C$, where $C$ is the constant of integration.
Steps to Solve
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Recognize the antiderivative of a constant
The antiderivative of a constant $c$ is given by the formula: $$ \int c , dx = cx + C $$ where $C$ is the constant of integration. -
Apply the constant value
For this problem, our constant $c$ is 5. We can use the formula: $$ \int 5 , dx = 5x + C $$ -
Final expression
Combine the information to write the final expression for the antiderivative of 5: $$ 5x + C $$
The antiderivative of 5 is $5x + C$, where $C$ is the constant of integration.
More Information
The antiderivative process is essential in calculus, allowing the recovery of original functions from their derivatives. In this case, any function of the form $5x + C$ will have a derivative of 5.
Tips
- Forgetting to include the constant of integration $C$. Always remember that the antiderivative is not unique and can vary by an additive constant.
- Confusing antiderivatives with derivatives. Ensure to distinguish between finding the original function and its rate of change.
