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Find the integral of cos(2x)dx. (2023)

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Question: Find the integral of cos(2x)dx. (2023)

Options:

  1. (1/2)sin(2x) + C
  2. sin(2x) + C
  3. (1/2)cos(2x) + C
  4. 2sin(2x) + C

Correct Answer: (1/2)sin(2x) + C

Solution: 

The integral of cos(kx) is (1/k)sin(kx) + C. Here, k=2, so the integral is (1/2)sin(2x) + C.

Find the integral of cos(2x)dx. (2023)

Practice Questions

Q1
Find the integral of cos(2x)dx. (2023)
  1. (1/2)sin(2x) + C
  2. sin(2x) + C
  3. (1/2)cos(2x) + C
  4. 2sin(2x) + C

Questions & Step-by-Step Solutions

Find the integral of cos(2x)dx. (2023)
  • Step 1: Identify the function you want to integrate, which is cos(2x).
  • Step 2: Recognize that the integral of cos(kx) is given by the formula (1/k)sin(kx) + C, where k is a constant.
  • Step 3: In this case, k is 2 because we have cos(2x).
  • Step 4: Substitute k = 2 into the formula: (1/2)sin(2x) + C.
  • Step 5: Write down the final answer: the integral of cos(2x)dx is (1/2)sin(2x) + C.
  • Integration of Trigonometric Functions – Understanding how to integrate functions like cos(kx) using the formula for the integral of cosine.
  • Constant Factor in Integration – Recognizing the role of the constant factor 'k' in the integration process and how it affects the result.
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