Evaluate the integral ∫ cos(5x) dx.

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Question: Evaluate the integral ∫ cos(5x) dx.

Options:

Correct Answer: 1/5 sin(5x) + C

Solution:

The integral of cos(kx) is (1/k)sin(kx). Here, k = 5, so ∫ cos(5x) dx = (1/5)sin(5x) + C.

Evaluate the integral ∫ cos(5x) dx.

Evaluate the integral ∫ cos(5x) dx.

Step 1: Identify the integral you need to evaluate, which is ∫ cos(5x) dx.
Step 2: Recognize that the integral of cos(kx) is given by the formula (1/k)sin(kx), where k is a constant.
Step 3: In this case, k is 5 because we have cos(5x).
Step 4: Apply the formula: Replace k with 5 in (1/k)sin(kx). This gives you (1/5)sin(5x).
Step 5: Don't forget to add the constant of integration, C, to your answer.
Step 6: Write the final answer: ∫ cos(5x) dx = (1/5)sin(5x) + C.

Integration of Trigonometric Functions – Understanding how to integrate functions like cos(kx) using the formula ∫ cos(kx) dx = (1/k)sin(kx) + C.