Question

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

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

l = $\int$ $\frac{1}{{sin}^{2010}x}$ ${sec}^{2}xdx$ - $\int$ $\frac{2010}{{sin}^{2010}x}$

= $\frac{tanx}{{sin}^{2010}x}+c$

$⟹f\left(x\right)=tanx$

$⟹$ f($\frac{\pi }{3}$) = $\sqrt{3}$