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Evaluate the definite integral ∫(1 to 2) (3x^2)dx.
Evaluate the definite integral ∫(1 to 2) (3x^2)dx.
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Practice Questions
1 question
Q1
Evaluate the definite integral ∫(1 to 2) (3x^2)dx.
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The integral evaluates to 6.
Questions & Step-by-step Solutions
1 item
Q
Q: Evaluate the definite integral ∫(1 to 2) (3x^2)dx.
Solution:
The integral evaluates to 6.
Steps: 7
Show Steps
Step 1: Identify the function to integrate, which is 3x^2.
Step 2: Find the antiderivative of 3x^2. The antiderivative is x^3.
Step 3: Evaluate the antiderivative at the upper limit (2). Calculate (2^3) = 8.
Step 4: Evaluate the antiderivative at the lower limit (1). Calculate (1^3) = 1.
Step 5: Subtract the value at the lower limit from the value at the upper limit. So, 8 - 1 = 7.
Step 6: Multiply the result by 3 (the coefficient in front of x^2). So, 3 * 7 = 21.
Step 7: The final answer is 21.
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