1. Tardigrade
  2. Question
  3. Mathematics
  4. ∫ limits-(π/2)(π/2) ( cos 2 2 x/1+25x) d x=

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. $\int\limits_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \frac{\cos ^{2} 2 x}{1+25^{x}} d x=$ _______

Gujarat CETGujarat CET 2019

Solution:

$\int\limits_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \frac{\cos ^{2} 2 x}{1+25^{x}} d x=\int\limits_{0}^{\frac{\pi}{2}} \frac{\cos ^{2} 2 x}{1+25^{x}}+\frac{\cos ^{2} 2 x}{1+25^{-x}} d x$
$=\int\limits_{0}^{\frac{\pi}{2}} \cos ^{2} 2 x d x$
$=\int\limits_{0}^{\frac{\pi}{2}} \frac{1+\cos 4 x}{2} d x$
$=\frac{1}{2}\left[x+\frac{\sin 4 x}{4}\right]_{0}^{\frac{\pi}{2}}=\frac{\pi}{4}$