The value of I=∫−π/2π/2 cos⁡ x−cos3⁡ xdx is

I=∫−π/2π/2 cos⁡ x|sin⁡ x|dx=2∫0π/2 cos⁡ x|sin⁡ x|dx(the integrand is an even function)=2∫0π/2 cos⁡ xsin⁡ xdx=−43(cos⁡ x)3/20π/2=43.