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Evaluate the integral ∫(x^2 - 2x + 1) dx. (2022)

Practice Questions

Q1
Evaluate the integral ∫(x^2 - 2x + 1) dx. (2022)
  1. (1/3)x^3 - x^2 + x + C
  2. (1/3)x^3 - x^2 + C
  3. (1/3)x^3 - 2x + C
  4. (1/3)x^3 - x^2 + x

Questions & Step-by-Step Solutions

Evaluate the integral ∫(x^2 - 2x + 1) dx. (2022)
  • Step 1: Identify the function to integrate, which is (x^2 - 2x + 1).
  • Step 2: Break down the integral into parts: ∫(x^2) dx, ∫(-2x) dx, and ∫(1) dx.
  • Step 3: Integrate each part separately.
  • Step 4: For ∫(x^2) dx, the result is (1/3)x^3.
  • Step 5: For ∫(-2x) dx, the result is -x^2.
  • Step 6: For ∫(1) dx, the result is x.
  • Step 7: Combine all the results: (1/3)x^3 - x^2 + x.
  • Step 8: Add the constant of integration, C, to the final result.
  • Step 9: Write the final answer as (1/3)x^3 - x^2 + x + C.
  • Polynomial Integration – The question tests the ability to integrate a polynomial function, specifically applying the power rule for integration.
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