Express the limit of sum: lim n→∞ (1/n) [1 + 2/n + 3/n + ... + n/n] as a definite integral. A. ∫[0 to 1] x² dx B. ∫[0 to 1] x dx C. ∫[0 to 1] 1/x dx D. ∫[0 to n] x dx Answer: B) ∫[0 to 1] x dx Explanation: This is a Riemann sum for f(x) = x over [0, 1]. The limit converts to the definite integral ∫[0 to 1] x dx.

imo class 12 definite integration

Express the limit of sum: lim n→∞ (1/n) [1 + 2/n + 3/n + ... + n/n] as a definite integral.

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Express the limit of sum: lim n→∞ (1/n) [1 + 2/n + 3/n + ... + n/n] as a definite integral.

Answer: B) ∫[0 to 1] x dx

Explanation: This is a Riemann sum for f(x) = x over [0, 1]. The limit converts to the definite integral ∫[0 to 1] x dx.