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1+cosx = 2[cos(x/2)]^2
∫(0->π^2) √(1+cosx) dx
=∫(0->π) √2.cos(x/2) dx -∫(π->3π) √2.cos(x/2) dx +∫(3π->π^2) √2.cos(x/2) dx
=2√2.[ sin(x/2)]|(0->π) -2√2.[ sin(x/2)]|(π->3π)+ 2√2.[ sin(x/2)]|(3π->π^2)
=2√2 +4√2 +2√2 [ sin(π^2/2) +1]
=8√2 +2√2.sin(π^2/2)
∫(0->π^2) √(1+cosx) dx
=∫(0->π) √2.cos(x/2) dx -∫(π->3π) √2.cos(x/2) dx +∫(3π->π^2) √2.cos(x/2) dx
=2√2.[ sin(x/2)]|(0->π) -2√2.[ sin(x/2)]|(π->3π)+ 2√2.[ sin(x/2)]|(3π->π^2)
=2√2 +4√2 +2√2 [ sin(π^2/2) +1]
=8√2 +2√2.sin(π^2/2)
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