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7.2 definite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.2 definite integral1 Mark
MCQ
$\mathop {\lim }\limits_{n \to \infty } \sum\limits_{r = 1}^n {\frac{1}{n}{e^{\frac{r}{n}}}} $ is
  • A
    $e + 1$
  • ✓
    $e - 1$
  • C
    $1 - e$
  • D
    $e$
✓

Answer

Correct option: B.
$e - 1$
b
(b) $\mathop {\lim }\limits_{n \to \infty } \sum\limits_{r = 1}^n {\frac{1}{n}{e^{\frac{r}{n}}} = \int_0^1 {{e^x}dx = [{e^x}]_0^1 = e - 1} } $.

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