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Evaluate ∫_1^2 (3x^2 - 4x + 1) dx.
Evaluate ∫_1^2 (3x^2 - 4x + 1) dx.
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Practice Questions
1 question
Q1
Evaluate ∫_1^2 (3x^2 - 4x + 1) dx.
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∫_1^2 (3x^2 - 4x + 1) dx = [x^3 - 2x^2 + x] from 1 to 2 = (8 - 8 + 2) - (1 - 2 + 1) = 1.
Questions & Step-by-step Solutions
1 item
Q
Q: Evaluate ∫_1^2 (3x^2 - 4x + 1) dx.
Solution:
∫_1^2 (3x^2 - 4x + 1) dx = [x^3 - 2x^2 + x] from 1 to 2 = (8 - 8 + 2) - (1 - 2 + 1) = 1.
Steps: 7
Show Steps
Step 1: Identify the integral you need to evaluate: ∫_1^2 (3x^2 - 4x + 1) dx.
Step 2: Find the antiderivative of the function 3x^2 - 4x + 1. The antiderivative is x^3 - 2x^2 + x.
Step 3: Write down the antiderivative with limits: [x^3 - 2x^2 + x] from 1 to 2.
Step 4: Calculate the value of the antiderivative at the upper limit (x = 2): 2^3 - 2(2^2) + 2 = 8 - 8 + 2 = 2.
Step 5: Calculate the value of the antiderivative at the lower limit (x = 1): 1^3 - 2(1^2) + 1 = 1 - 2 + 1 = 0.
Step 6: Subtract the lower limit result from the upper limit result: 2 - 0 = 2.
Step 7: The final answer is 2.
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