Final answer:
To find the indefinite integral of 36 - 4x² dx, integrate each term separately to get 36x as the integral of 36, and -4/3x³ as the integral of -4x². The final answer is 36x - 4/3x³ + c, where c represents the constant of integration.
Step-by-step explanation:
The indefinite integral of a function is found by finding a function whose derivative gives us the original function. In this case, to integrate 36 - 4x² with respect to x, we would integrate each term separately.
The integral of a constant, such as 36, is that constant times the variable of integration, so the integral of 36 is 36x. For the term -4x², we would use the power rule of integration, which states that the integral of xⁿ is xⁿ⁺÷(n + 1), unless n is -1, in which case the integral is the natural logarithm of the absolute value of x. Hence, the integral of -4x² is -4/3x³.
Putting it all together, the indefinite integral of 36 - 4x² dx is 36x - 4/3x³ + c, where c is the constant of integration.