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What is the integral of e^(2x)? (2023)

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Question: What is the integral of e^(2x)? (2023)

Options:

  1. (1/2)e^(2x) + C
  2. 2e^(2x) + C
  3. e^(2x) + C
  4. (1/2)e^(x) + C

Correct Answer: (1/2)e^(2x) + C

Exam Year: 2023

Solution: 

The integral of e^(2x) is (1/2)e^(2x) + C.

What is the integral of e^(2x)? (2023)

Practice Questions

Q1
What is the integral of e^(2x)? (2023)
  1. (1/2)e^(2x) + C
  2. 2e^(2x) + C
  3. e^(2x) + C
  4. (1/2)e^(x) + C

Questions & Step-by-Step Solutions

What is the integral of e^(2x)? (2023)
  • Step 1: Identify the function to integrate, which is e^(2x).
  • Step 2: Recall the rule for integrating exponential functions: the integral of e^(kx) is (1/k)e^(kx) + C, where k is a constant.
  • Step 3: In our case, k is 2 because we have e^(2x).
  • Step 4: Apply the rule: since k = 2, the integral becomes (1/2)e^(2x) + C.
  • Step 5: Write down the final answer: the integral of e^(2x) is (1/2)e^(2x) + C.
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