∫√(a^2-x^2)dx
设x=asint
则dx=dasint=acostdt
a^2-x^2
=a^2-a^2sint^2
=a^2cost^2
∫√(a^2-x^2)dx
=∫acost*acostdt
=a^2∫cost^2dt
=a^2∫(cos2t+1)/2dt
=a^2/4∫(cos2t+1)d2t
=a^2/4*(sin2t+2t)
将x=asint代回
∫√(a^2-x^2)dx=x√(a^2-x^2)/2+a^2*arcsin(x/a)/2
∫√(a^2-x^2)dx
设x=asint
则dx=dasint=acostdt
a^2-x^2
=a^2-a^2sint^2
=a^2cost^2
∫√(a^2-x^2)dx
=∫acost*acostdt
=a^2∫cost^2dt
=a^2∫(cos2t+1)/2dt
=a^2/4∫(cos2t+1)d2t
=a^2/4*(sin2t+2t)
将x=asint代回
∫√(a^2-x^2)dx=x√(a^2-x^2)/2+a^2*arcsin(x/a)/2