If is integrable over [1,2] , then _ 1 ^ 2 f(x) d x is equal to
Mathematics · JEE Advanced · NTA Exams — Integral Calculus
If 
is integrable over \([1,2]\), then \(\int_{1}^{2} f(x) d x\) is equal to
is integrable over \([1,2]\), then \(\int_{1}^{2} f(x) d x\) is equal to- \(\lim _{n \rightarrow \infty} \frac{1}{n} \sum_{r=1}^{n} f\left(\frac{r}{n}\right)\)
- \(\lim _{n \rightarrow \infty} \frac{1}{n} \sum_{r=n+1}^{2 n} f\left(\frac{r}{n}\right)\)
- \(\lim _{n \rightarrow \infty} \frac{1}{n} \sum_{r=1}^{n} f\left(\frac{r+n}{n}\right)\)
- \(\lim _{n \rightarrow \infty} \frac{1}{n} \sum_{r=1}^{2 n} f\left(\frac{r}{n}\right)\)
Answer
(B) _ n 1 n _ r=n+1 ^ 2 n f ( r n ), (C) _ n 1 n _ r=1 ^ n f ( r+n n )
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