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Evaluate the integral ∫(1 to 2) (3x^2 - 2)dx.
Evaluate the integral ∫(1 to 2) (3x^2 - 2)dx.
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Practice Questions
1 question
Q1
Evaluate the integral ∫(1 to 2) (3x^2 - 2)dx.
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The integral evaluates to [(x^3 - 2x)] from 1 to 2 = (8 - 4) - (1 - 2) = 5.
Questions & Step-by-step Solutions
1 item
Q
Q: Evaluate the integral ∫(1 to 2) (3x^2 - 2)dx.
Solution:
The integral evaluates to [(x^3 - 2x)] from 1 to 2 = (8 - 4) - (1 - 2) = 5.
Steps: 5
Show Steps
Step 1: Identify the integral to evaluate: ∫(1 to 2) (3x^2 - 2)dx.
Step 2: Find the antiderivative of the function 3x^2 - 2. The antiderivative is x^3 - 2x.
Step 3: Evaluate the antiderivative at the upper limit (x = 2): (2^3 - 2*2) = (8 - 4) = 4.
Step 4: Evaluate the antiderivative at the lower limit (x = 1): (1^3 - 2*1) = (1 - 2) = -1.
Step 5: Subtract the value at the lower limit from the value at the upper limit: 4 - (-1) = 4 + 1 = 5.
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