Concept Explanation:
The antiderivative (indefinite integral) of a function \( f(x) \) is a family of functions \( F(x) \) such that \[ F'(x) = f(x). \] The constant of integration \( C \) shifts the antiderivative vertically: \[ F(x) = \int f(x)\,dx + C. \] In this example, \[ f(x) = 2x + 1, \quad F(x) = x^2 + x + C. \] This visualization shows both \( f(x) \) (blue line) and its antiderivative \( F(x) \) (red line). Move the slider to see how the constant \( C \) changes the vertical position of \( F(x) \).

Constant C: 0

Quiz Question

The function is f(x) = 2x + 1. An antiderivative is F(x) = x² + x + C.
If C = 3, what is the value of F(2)?

A. 5
B. 9
C. 13
D. 21

Check Answer