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