What is the result of computing ∫ (4x^3 - 3) dx?

What is the result of computing ∫ (4x^3 - 3) dx?

• A. x^4 - 3x + C
• B. 4x^4 - 3x + C
• C. x^4 - 3 + C
• D. (1/4)x^4 - 3x + C

Answer: (A)

To determine the integral of the given polynomial function, we will integrate term by term. The integral in question is ∫ (4x^3 - 3) dx. We can break this down into two separate integrals: 1. ∫ 4x^3 dx 2. ∫ -3 dx Starting with the first integral, ∫ 4x^3 dx, we apply the power rule of integration, which states that the integral of x^n is (1/(n+1))x^(n+1) plus a constant of integration. Here, n is 3: ∫ 4x^3 dx = 4 * (1/(3+1)) x^(3+1) = 4 * (1/4) x^4 = x^4. Next, we compute the integral of the constant term, ∫ -3 dx, which results in: ∫ -3 dx = -3x. Now, combining these results, we have: ∫ (4x^3 - 3) dx = x^4 - 3x + C, where C is the constant of integration. This result aligns perfectly with one of the provided choices, confirming that

To determine the integral of the given polynomial function, we will integrate term by term.

The integral in question is ∫ (4x^3 - 3) dx. We can break this down into two separate integrals:

1. ∫ 4x^3 dx

2. ∫ -3 dx

Starting with the first integral, ∫ 4x^3 dx, we apply the power rule of integration, which states that the integral of x^n is (1/(n+1))x^(n+1) plus a constant of integration. Here, n is 3:

∫ 4x^3 dx = 4 * (1/(3+1)) x^(3+1) = 4 * (1/4) x^4 = x^4.

Next, we compute the integral of the constant term, ∫ -3 dx, which results in:

∫ -3 dx = -3x.

Now, combining these results, we have:

∫ (4x^3 - 3) dx = x^4 - 3x + C, where C is the constant of integration.

This result aligns perfectly with one of the provided choices, confirming that