calculate-I-0-2pi-cos-4x-cosx-sinx-and-J-0-2pi-sin-4x-cosx-sinx-dx-

Question Number 42501 by maxmathsup by imad last updated on 26/Aug/18

c a l c u l a t e I = \int_{0}^{2 π} \frac{c o s (4 x)}{c o s x + s i n x} a n d J = \int_{0}^{2 π} \frac{s i n (4 x)}{c o s x + s i n x} d x

Commented by maxmathsup by imad last updated on 27/Aug/18

w e h a v e I = \int_{0}^{π} \frac{c o s (4 x)}{c o s x + s i n x} d x + \int_{π}^{2 π} \frac{c o s (4 x)}{c o s x + s i n x} b u t c h a n g e m e n t

x = π + t g i v e \int_{π}^{2 π} \frac{c o s (4 x)}{c o s x + s i n x} d x = \int_{0}^{π} \frac{c o s (4 t)}{- c o s t - s i n t} d t \Rightarrow I = 0

t h e s a m e m e t h o d s h o w t h a t J = 0