The value of $\int\limits_{-10}^{10} \frac{3^x}{3^{[x]}} d x$ is equal to (where [.] denotes greatest integer function) :

20 $\frac{40}{\ln 3}$ $\frac{20}{\ln 3}$ none of these

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

$I=\int\limits_{-10}^{10} 3^{x-[x]} dx=20 \int\limits_0^1 3^{x-[x]} dx=20 \int\limits_0^1 3^x dx$ $=20\left|\frac{3^x}{\ln 3}\right|_0^1=20 \frac{1}{\ln 3}(3-1)=\frac{40}{\ln 3}$ Hence (2) is the correct answer.