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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?
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Practice Questions
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Q1
What is the value of the integral ∫(2x)dx from 0 to 1?
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∫(2x)dx = x^2 from 0 to 1 = 1^2 - 0^2 = 1.
Questions & Step-by-step Solutions
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Q
Q: What is the value of the integral ∫(2x)dx from 0 to 1?
Solution:
∫(2x)dx = x^2 from 0 to 1 = 1^2 - 0^2 = 1.
Steps: 7
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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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