Final answer:
The integral of the function 1 - 25x² is x - 8.333x³ + c, where c is the constant of integration.
Step-by-step explanation:
The integral of the function 1 - 25x² with respect to x can be evaluated by integrating each term separately. Remember that the integral of a constant is just the constant times x, and the integral of x² is x³/3. So, it will look something like this:
∫(1 - 25x²) dx = ∫1 dx - ∫25x² dx = x - ⅓(25x³) + c = x - ⅓ * 25 * x³ + c = x - ⅓ * 25x³ + c.
Thus, the antiderivative of 1 - 25x² is x - ⅓ * 25x³ + c, where c is the constant of integration.