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Evaluate the integral ∫ cos(3x) dx.

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Question: Evaluate the integral ∫ cos(3x) dx.

Options:

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

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

Solution: 

The integral of cos(kx) is (1/k)sin(kx). Here, k = 3, so ∫ cos(3x) dx = (1/3)sin(3x) + C.

Evaluate the integral ∫ cos(3x) dx.

Practice Questions

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

Questions & Step-by-Step Solutions

Evaluate the integral ∫ cos(3x) dx.
  • Step 1: Identify the integral you need to evaluate, which is ∫ cos(3x) dx.
  • Step 2: Recognize that the integral of cos(kx) is (1/k)sin(kx), where k is a constant.
  • Step 3: In this case, k is 3 because we have cos(3x).
  • Step 4: Substitute k = 3 into the formula: ∫ cos(3x) dx = (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: ∫ cos(3x) dx = (1/3)sin(3x) + C.
  • Integration of Trigonometric Functions – Understanding how to integrate functions like cos(kx) using the formula ∫ cos(kx) dx = (1/k)sin(kx) + C.
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