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Evaluate the definite integral ∫(0 to 1) (3x^2)dx.
Evaluate the definite integral ∫(0 to 1) (3x^2)dx.
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Practice Questions
1 question
Q1
Evaluate the definite integral ∫(0 to 1) (3x^2)dx.
1
0.5
0.33
0.25
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The integral evaluates to 1.
Questions & Step-by-step Solutions
1 item
Q
Q: Evaluate the definite integral ∫(0 to 1) (3x^2)dx.
Solution:
The integral evaluates to 1.
Steps: 6
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 (1) and lower limit (0).
Step 4: Calculate the value at the upper limit: (1)^3 = 1.
Step 5: Calculate the value at the lower limit: (0)^3 = 0.
Step 6: Subtract the lower limit value from the upper limit value: 1 - 0 = 1.
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