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What is the value of the integral ∫(2x)dx from 0 to 2?
What is the value of the integral ∫(2x)dx from 0 to 2?
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Practice Questions
1 question
Q1
What is the value of the integral ∫(2x)dx from 0 to 2?
4
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3
1
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∫(2x)dx = x^2 from 0 to 2 = 2^2 - 0^2 = 4.
Questions & Step-by-step Solutions
1 item
Q
Q: What is the value of the integral ∫(2x)dx from 0 to 2?
Solution:
∫(2x)dx = x^2 from 0 to 2 = 2^2 - 0^2 = 4.
Steps: 6
Show Steps
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 2.
Step 4: Evaluate the antiderivative at the upper limit (2): (2)^2 = 4.
Step 5: Evaluate the antiderivative at the lower limit (0): (0)^2 = 0.
Step 6: Subtract the value at the lower limit from the value at the upper limit: 4 - 0 = 4.
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