_ - 10 ^ 10 3^x 3^ [x] ,dx is equal to, where [·] is G.I.F. - Vidyadip

MCQ

$\int\limits_{ - 10}^{10} {\frac{{{3^x}}}{{{3^{[x]}}}}\,dx} $ is equal to, where $[·]$ is $G.I.F.$

A
$20$
✓
$\frac{40}{ln3}$
C
$\frac{20}{ln3}$
D
None of these

✓

Answer

Correct option: B.

$\frac{40}{ln3}$

b
$\int_{-10}^{10} 3^{\{x\}} d x$

$ = 20\int_0^1 {{3^x}} dx = \frac{{20}}{{\ln 3}}\left( {{3^x}} \right)_0^1$

$ = \frac{{20}}{{\ln 3}}(3 - 1)$

$=\frac{40}{\ln 3}$

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