The antiderivative of 2x is a fundamental concept in calculus. To find the antiderivative, we need to determine a function whose derivative is 2x.
The antiderivative of 2x is given by:
∫2x dx = x² + C
Here, ∫ represents the integral sign, 2x is the function we are integrating, dx indicates that we are integrating with respect to x, and C is the constant of integration.
Explanation:
- The derivative of x² is 2x. Therefore, the antiderivative of 2x is x².
- The constant of integration, C, is added because the derivative of a constant is zero. This means that there are infinitely many antiderivatives, each differing by a constant.
In summary, the antiderivative of 2x is x² + C, where C is any constant.