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Find the integral ∫ sin(2x) dx.
Find the integral ∫ sin(2x) dx.
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Practice Questions
1 question
Q1
Find the integral ∫ sin(2x) dx.
-cos(2x)/2 + C
cos(2x)/2 + C
-sin(2x)/2 + C
sin(2x)/2 + C
Show Solution
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The integral of sin(kx) is -1/k * cos(kx). Here, k = 2, so ∫ sin(2x) dx = -cos(2x)/2 + C.
Questions & Step-by-step Solutions
1 item
Q
Q: Find the integral ∫ sin(2x) dx.
Solution:
The integral of sin(kx) is -1/k * cos(kx). Here, k = 2, so ∫ sin(2x) dx = -cos(2x)/2 + C.
Steps: 6
Show Steps
Step 1: Identify the function to integrate, which is sin(2x).
Step 2: Recognize that the integral of sin(kx) is -1/k * cos(kx), where k is a constant.
Step 3: In this case, k is 2 because we have sin(2x).
Step 4: Substitute k = 2 into the formula: the integral becomes -1/2 * cos(2x).
Step 5: Don't forget to add the constant of integration, C, to the result.
Step 6: Write the final answer: ∫ sin(2x) dx = -cos(2x)/2 + C.
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