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What is the integral of cos(3x) dx?

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Question: What is the integral of cos(3x) dx?

Options:

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

Correct Answer: (1/3)sin(3x) + C

Solution: 

The integral of cos(3x) is (1/3)sin(3x) + C, where C is the constant of integration.

What is the integral of cos(3x) dx?

Practice Questions

Q1
What is the integral of cos(3x) dx?
  1. (1/3)sin(3x) + C
  2. 3sin(3x) + C
  3. (1/3)cos(3x) + C
  4. sin(3x) + C

Questions & Step-by-Step Solutions

What is the integral of cos(3x) dx?
  • Step 1: Identify the function you want to integrate, which is cos(3x).
  • Step 2: Recognize that the integral of cos(kx) is (1/k)sin(kx) for any constant k.
  • Step 3: In this case, k is 3, so we will use k = 3 in our formula.
  • Step 4: Apply the formula: the integral of cos(3x) is (1/3)sin(3x).
  • Step 5: Don't forget to add the constant of integration, C, to your answer.
  • Step 6: Write the final answer: (1/3)sin(3x) + C.
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