Question

If ${\int }_0^{60}\frac{dx}{2x+1}=\log a$, then $a=$

• A. $3$
• B. $11$
• C. $81$
• D. $40$

Answer 1

The correct option is B $11$

Let $I={\int }_0^{60}\frac{dx}{2x+1}$
$={\left[\frac{\log (2x+1)}{2}\right]}_0^{60}$
$=\frac{1}{2}\left[\log \right(121)-\log (1\left)\right]$
$=\frac{\log \left(121\right)}{2}$
$=\log \left(\sqrt{121}\right)$
$=\log 11$
Thus $\log 11=\log a$
$\Rightarrow a=11$