calculus problem?

x²+y²=a² about x axis
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x²+y²=a²
x = acosθ　dx = -asinθ dθ　dx/dθ = -asinθ
y = asinθ　dy = acosθ dθ　dy/dθ = acosθ



∫[θ=0 to π] 2πy((dx/dθ)² + (dy/dθ)²)^(1/2) dθ

= ∫[x=0 to π] 2πasinθ * ((-asinθ)² + (acosθ)²)^(1/2) dθ

= ∫[x=0 to π] 2πasinθ * a dθ

= 2πa² ∫[x=0 to π] sinθ dθ

= 2πa² [-cosθ] from x=0 to π

= 2πa²(1+1)

= 4πa²