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Evaluate ∫ (5 - 3x) dx. (2022)

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Question: Evaluate ∫ (5 - 3x) dx. (2022)

Options:

  1. 5x - (3/2)x^2 + C
  2. 5x - (3/3)x^2 + C
  3. 5x - (3/4)x^2 + C
  4. 5x - (3/5)x^2 + C

Correct Answer: 5x - (3/2)x^2 + C

Solution: 

The integral is 5x - (3/2)x^2 + C.

Evaluate ∫ (5 - 3x) dx. (2022)

Practice Questions

Q1
Evaluate ∫ (5 - 3x) dx. (2022)
  1. 5x - (3/2)x^2 + C
  2. 5x - (3/3)x^2 + C
  3. 5x - (3/4)x^2 + C
  4. 5x - (3/5)x^2 + C

Questions & Step-by-Step Solutions

Evaluate ∫ (5 - 3x) dx. (2022)
  • Step 1: Identify the function to integrate, which is (5 - 3x).
  • Step 2: Break down the integral into two parts: ∫5 dx and ∫(-3x) dx.
  • Step 3: Integrate the first part, ∫5 dx, which gives 5x.
  • Step 4: Integrate the second part, ∫(-3x) dx. The integral of x is (1/2)x^2, so this part becomes -3 * (1/2)x^2 = -(3/2)x^2.
  • Step 5: Combine the results from Step 3 and Step 4: 5x - (3/2)x^2.
  • Step 6: Add the constant of integration, C, to the final result.
  • Integration of Polynomials – The question tests the ability to integrate a linear polynomial function.
  • Constant of Integration – The importance of including the constant of integration (C) in indefinite integrals.
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