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Question 340008
JEE Mathematics · Hard

Definite Integration and Area: Periodic function MCQ

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Periodic functionHardQuestion 340008

Question

If f(x) has period T, then ∫₀^(nT) f(x) dx equals:
  1. A
    n ∫₀ᵀ f(x) dx
    Correct
  2. B
    ∫₀ᵀ f(x) dx
  3. C
    n²∫₀ᵀ f(x) dx
  4. D
    Depends on n

Correct answer

n ∫₀ᵀ f(x) dx

Explanation

For a function with period T: ∫₀^(nT) f(x) dx = n × ∫₀ᵀ f(x) dx. Each complete period contributes the same integral.

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