WBJEE · Maths · Definite Integration
Let \(f\), be a continuous function in \([0,1]\), then \(\lim_{n \rightarrow \infty} \sum_{j=0}^n \frac{1}{n} f\left(\frac{j}{n}\right)\) is
- A \(\frac{1}{2} \int_{0}^{\frac{1}{2}} \mathrm{f}(\mathrm{x}) \mathrm{dx}\)
- B \(\int_{\frac{1}{2}}^{1} \mathrm{f}(\mathrm{x}) \mathrm{dx}\)
- C \(\int_{0}^{1} f(x) d x\)
- D \(\int_{0}^{\frac{1}{2}} \mathrm{f}(\mathrm{x}) \mathrm{dx}\)
Answer & Solution
Correct Answer
(C) \(\int_{0}^{1} f(x) d x\)
Step-by-step Solution
Detailed explanation
\(\lim _{n \rightarrow \infty} \sum_{i=0}^{n} \frac{1}{n} f\left(\frac{i}{n}\right)\) Let \(1 / n \rightarrow d x\)
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