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Find the integral of (2x + 3)dx. (2022)

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Question: Find the integral of (2x + 3)dx. (2022)

Options:

  1. x^2 + 3x + C
  2. x^2 + 3x + 1
  3. x^2 + 3 + C
  4. 2x^2 + 3x + C

Correct Answer: x^2 + 3x + C

Exam Year: 2022

Solution: 

Integrating term by term: ∫2xdx = x^2 and ∫3dx = 3x. Thus, ∫(2x + 3)dx = x^2 + 3x + C.

Find the integral of (2x + 3)dx. (2022)

Practice Questions

Q1
Find the integral of (2x + 3)dx. (2022)
  1. x^2 + 3x + C
  2. x^2 + 3x + 1
  3. x^2 + 3 + C
  4. 2x^2 + 3x + C

Questions & Step-by-Step Solutions

Find the integral of (2x + 3)dx. (2022)
  • Step 1: Identify the function to integrate, which is (2x + 3).
  • Step 2: Break the integral into two parts: ∫(2x + 3)dx = ∫2xdx + ∫3dx.
  • Step 3: Integrate the first part, ∫2xdx. The integral of 2x is x^2.
  • Step 4: Integrate the second part, ∫3dx. The integral of 3 is 3x.
  • Step 5: Combine the results from Step 3 and Step 4. You get x^2 + 3x.
  • Step 6: Add the constant of integration, C, to the final result. The final answer is x^2 + 3x + C.
  • Integration – The process of finding the integral of a function, which involves determining the antiderivative.
  • Term-by-term integration – The method of integrating each term of a polynomial separately.
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