Find the value of ∫ from 0 to 1 of (x^2 - 2x + 1) dx.
Practice Questions
1 question
Q1
Find the value of ∫ from 0 to 1 of (x^2 - 2x + 1) dx.
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The integral evaluates to [x^3/3 - x^2 + x] from 0 to 1 = (1/3 - 1 + 1) = 1/3.
Questions & Step-by-step Solutions
1 item
Q
Q: Find the value of ∫ from 0 to 1 of (x^2 - 2x + 1) dx.
Solution: The integral evaluates to [x^3/3 - x^2 + x] from 0 to 1 = (1/3 - 1 + 1) = 1/3.
Steps: 6
Step 1: Identify the function to integrate, which is (x^2 - 2x + 1).
Step 2: Find the antiderivative of the function. The antiderivative of x^2 is x^3/3, the antiderivative of -2x is -x^2, and the antiderivative of 1 is x.
Step 3: Combine the antiderivatives to get the complete antiderivative: (x^3/3 - x^2 + x).
Step 4: Evaluate the antiderivative from the lower limit (0) to the upper limit (1).
Step 5: Substitute the upper limit (1) into the antiderivative: (1^3/3 - 1^2 + 1) = (1/3 - 1 + 1).
