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What is the integral of f(x) = 2x from 0 to 3?

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Question: What is the integral of f(x) = 2x from 0 to 3?

Options:

  1. 9
  2. 6
  3. 3
  4. 12

Correct Answer: 6

Solution: 

∫(2x)dx from 0 to 3 = [x^2] from 0 to 3 = 9 - 0 = 9.

What is the integral of f(x) = 2x from 0 to 3?

Practice Questions

Q1
What is the integral of f(x) = 2x from 0 to 3?
  1. 9
  2. 6
  3. 3
  4. 12

Questions & Step-by-Step Solutions

What is the integral of f(x) = 2x from 0 to 3?
  • Step 1: Identify the function to integrate, which is f(x) = 2x.
  • Step 2: Set up the integral from 0 to 3: ∫(2x)dx from 0 to 3.
  • Step 3: Find the antiderivative of 2x. The antiderivative is x^2.
  • Step 4: Evaluate the antiderivative at the upper limit (3): (3)^2 = 9.
  • Step 5: Evaluate the antiderivative at the lower limit (0): (0)^2 = 0.
  • Step 6: Subtract the lower limit result from the upper limit result: 9 - 0 = 9.
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