定积分应用,求第四题平面图形面积

S=∫[a(1 - cos t)][a(1 - cos t)dt]
=(a^2)∫(1 - cos t)^2dt
=4(a^2)∫[sin(t/2)]^4dt(令t=2u)
=8(a^2)∫[(sinu)^4]du
=16(a^2)∫[(sinu)^4]du
=16(a^2)(3/4)(1/2)(π/2)
=3πa^2.