Final answer:
To find the antiderivative of the function 18t², we integrate the function using the power rule to get 6t³, and then add a constant of integration, resulting in the final answer 6t³ + C.
Step-by-step explanation:
To find an antiderivative of the function 18t², we want to find a function whose derivative is 18t². The process of finding an antiderivative is also known as integration. According to the power rule of integration, if we have a function of the form at^n, an antiderivative would be (a/(n+1))t^(n+1), since when we differentiate it, we return to the original function at^n.
In this case, the antiderivative of 18t² would be (18/3)t^(2+1), which simplifies to 6t^3. However, when finding antiderivatives, we must remember to add a constant of integration, denoted as C, because the derivative of a constant is zero, and thus it does not appear in the original function. So, the final answer is the antiderivative of 18t² is 6t³ + C.