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Shortcut used: Identify whether the problem needs an antiderivative, definite integral, approximation, or accumulation theorem.
Solve in 3 steps:
- Mark the given values and the exact target.
- Apply the relevant formula, rule, or concept.
- Check the final value against the options.
Common mistake: Do not choose an option before confirming the exact demand of the question.
Question 9
Multiple Choice Question
Question
What is the average value of f(x)=x^2 on [0,3]?
Explanation
Correct Answer: A
ANSWER
Correct Answer: A
Method / Topic: Integrals
Average value is (1/3)∫0^3x^2dx=(1/3)(9)=3.
Why this answer is correct
The correct option matches the required rule and the given information.
Short Explanation
Average value is (1/3)∫0^3x^2dx=(1/3)(9)=3.
Detailed Explanation
Question
What is the average value of f(x)=x^2 on [0,3]?
ANSWER
Correct Answer: A
Method / Topic: Integrals
Average value is (1/3)∫0^3x^2dx=(1/3)(9)=3.
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Question 9
Learn + Solve: Shortcut, Trap & Fast Route Click to view shortcut, steps, and common mistake
Learn + solve
Shortcut used, common trap, and the fastest solving route
Shortcut used: Identify whether the problem needs an antiderivative, definite integral, approximation, or accumulation theorem.
Solve in 3 steps:
- Mark the given values and the exact target.
- Apply the relevant formula, rule, or concept.
- Check the final value against the options.
Common mistake: Do not choose an option before confirming the exact demand of the question.
Question
What is the average value of f(x)=x^2 on [0,3]?
Explanation
Correct Answer: A
ANSWER
Correct Answer: A
Method / Topic: Integrals
Average value is (1/3)∫0^3x^2dx=(1/3)(9)=3.
Why this answer is correct
The correct option matches the required rule and the given information.
Short Explanation
Average value is (1/3)∫0^3x^2dx=(1/3)(9)=3.
Detailed Explanation
Question
What is the average value of f(x)=x^2 on [0,3]?
ANSWER
Correct Answer: A
Method / Topic: Integrals
Average value is (1/3)∫0^3x^2dx=(1/3)(9)=3.
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Concept tagged
definite integral
approximation
or accumulation theorem.