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Find the indefinite integral of 36 - 4x² dx. (Use c for the constant of integration.)

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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.

User Vyktor
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