Final answer:
To find the antiderivatives of G(t) = 4, we obtain 4t + C, where C is an arbitrary constant. By taking the derivative of 4t + C, we re-obtain G(t) = 4, confirming the correctness of the antiderivative.
Step-by-step explanation:
The question involves finding all the antiderivatives of the constant function G(t) = 4. The antiderivative of a constant function is a linear function. For the antiderivative of 4, we get the function 4t + C, where C is the arbitrary constant that must be included to represent the general solution for an antiderivative.
To validate our antiderivative, we take the derivative of 4t + C with respect to t. The derivative of 4t with respect to t is 4, and the derivative of a constant C is 0. Hence, the derivative of 4t + C is just 4, which confirms that our antiderivative is correct since it matches the original function G(t).
The process of finding an antiderivative is essentially the reverse of differentiation, and checking it by differentiation is a way to ensure the correctness of our antiderivative.