Question

The value of ${\int }_{-10}^{10}\frac{3^x}{3^{\left[x\right]}}dx$ is equal to?

• A. $20$
• B. $\frac{40}{ln3}$
• C. $\frac{20}{ln3}$
• D. $\frac{60}{ln3}$

Answer 1

The correct option is B $\frac{40}{ln3}$

${\int }_{-10}^{10}\frac{3^x}{3\left(x\right)}dx$

${\int }_{-10}^{10}{3}^{x-\left(x\right)}dx$ as even function

$=2{\int }_0^{10}{3}^{x-\left[x\right]}dx$

$2\times 10{\int }_0^1{3}^{x}dx$

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

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

$=\frac{20\times 2}{\ln 3}=\frac{40}{\ln 3}$