Evaluate the integral ∫ (3x^2 - 4) dx.

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Question: Evaluate the integral ∫ (3x^2 - 4) dx.

Options:

Correct Answer: x^3 - 4x + C

Solution:

The integral evaluates to x^3 - 4x + C, where C is the constant of integration.

Evaluate the integral ∫ (3x^2 - 4) dx.

Evaluate the integral ∫ (3x^2 - 4) dx.

Step 1: Identify the function to integrate, which is 3x^2 - 4.
Step 2: Apply the power rule of integration. For any term ax^n, the integral is (a/n+1)x^(n+1).
Step 3: For the term 3x^2, apply the power rule: the integral is (3/3)x^(2+1) = x^3.
Step 4: For the constant term -4, the integral is -4x, since the integral of a constant a is ax.
Step 5: Combine the results from Step 3 and Step 4: x^3 - 4x.
Step 6: Add the constant of integration, C, to the result: x^3 - 4x + C.

Integration of Polynomials – The question tests the ability to integrate polynomial functions, specifically applying the power rule for integration.