Evaluate ∫ (4x^3 - 2x) dx. (2019)

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Question: Evaluate ∫ (4x^3 - 2x) dx. (2019)

Options:

Correct Answer: x^4 - x^2 + C

Solution:

The integral is (4/4)x^4 - (2/2)x^2 + C = x^4 - x^2 + C.

Evaluate ∫ (4x^3 - 2x) dx. (2019)

Evaluate ∫ (4x^3 - 2x) dx. (2019)

Step 1: Identify the integral you need to evaluate: ∫ (4x^3 - 2x) dx.
Step 2: Break the integral into two parts: ∫ 4x^3 dx and ∫ -2x dx.
Step 3: For the first part, use the power rule of integration: ∫ x^n dx = (1/(n+1))x^(n+1) + C. Here, n = 3.
Step 4: Apply the power rule to ∫ 4x^3 dx: (4/(3+1))x^(3+1) = (4/4)x^4 = x^4.
Step 5: For the second part, apply the power rule to ∫ -2x dx: (−2/(1+1))x^(1+1) = (−2/2)x^2 = -x^2.
Step 6: Combine the results from Step 4 and Step 5: x^4 - x^2.
Step 7: Don't forget to add the constant of integration, C: Final result is x^4 - x^2 + C.

Integration of Polynomials – The question tests the ability to integrate polynomial functions using the power rule.