What is the value of the integral ∫(2x)dx from 0 to 1?

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Question: What is the value of the integral ∫(2x)dx from 0 to 1?

Options:

Correct Answer: 1

Solution:

∫(2x)dx = x^2 from 0 to 1 = 1^2 - 0^2 = 1.

What is the value of the integral ∫(2x)dx from 0 to 1?

What is the value of the integral ∫(2x)dx from 0 to 1?

Step 1: Identify the integral you need to solve, which is ∫(2x)dx.
Step 2: Find the antiderivative of 2x. The antiderivative of 2x is x^2.
Step 3: Write down the limits of integration, which are from 0 to 1.
Step 4: Evaluate the antiderivative at the upper limit (1): x^2 = 1^2 = 1.
Step 5: Evaluate the antiderivative at the lower limit (0): x^2 = 0^2 = 0.
Step 6: Subtract the value at the lower limit from the value at the upper limit: 1 - 0 = 1.
Step 7: The value of the integral ∫(2x)dx from 0 to 1 is 1.

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