Question

If $\int \frac{se{c}^{2}x-2010}{si{n}^{2010}x}dx=\frac{f\left(x\right)}{si{n}^{2010}x}+c$, then $f\left(\frac{\pi }{3}\right)=$ is

• A. $\sqrt{3}$
• B. $\frac{1}{\sqrt{3}}$
• C. $\frac{1}{2}$
• D. $\frac{\sqrt{3}}{2}$

Answer 1

The correct option is A $\sqrt{3}$

$I=\int \frac{1}{si{n}^{2010}x}se{c}^{2}xdx-\int \frac{2010}{si{n}^{2010}x}dx$
$=\frac{tanx}{si{n}^{2010}x}+c\Rightarrow f\left(x\right)=tanx\Rightarrow f\left(\frac{\pi }{3}\right)=\sqrt{3}$