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Evaluate the integral ∫_1^2 (3x^2 - 2) dx.
Evaluate the integral ∫_1^2 (3x^2 - 2) dx.
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Practice Questions
1 question
Q1
Evaluate the integral ∫_1^2 (3x^2 - 2) dx.
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∫_1^2 (3x^2 - 2) dx = [x^3 - 2x] from 1 to 2 = (8 - 4) - (1 - 2) = 3.
Questions & Step-by-step Solutions
1 item
Q
Q: Evaluate the integral ∫_1^2 (3x^2 - 2) dx.
Solution:
∫_1^2 (3x^2 - 2) dx = [x^3 - 2x] from 1 to 2 = (8 - 4) - (1 - 2) = 3.
Steps: 6
Show Steps
Step 1: Identify the integral to evaluate: ∫_1^2 (3x^2 - 2) dx.
Step 2: Find the antiderivative of the function 3x^2 - 2. The antiderivative is x^3 - 2x.
Step 3: Write the expression for the definite integral using the antiderivative: [x^3 - 2x] from 1 to 2.
Step 4: Substitute the upper limit (2) into the antiderivative: (2^3 - 2*2) = (8 - 4) = 4.
Step 5: Substitute the lower limit (1) into the antiderivative: (1^3 - 2*1) = (1 - 2) = -1.
Step 6: Calculate the difference between the upper and lower limits: 4 - (-1) = 4 + 1 = 5.
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