S₁=2∫(π/2,0)cosxdx=2sin(x)|(π/2,0)=2
S₂=∫(π,0)sinxdx=-cos(x)|(π,0)=2
S₃=∫(π/4,0)sinxdx=-cos(x)|(π/4,0)=1-√2/2
S₄=∫(π/2,π/4)cosxdx=sin(x)|(π/2,π/4)=1-√2/2
∴S=4-2+√2=2+√2
