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化极坐标。
I = ∫<-π/2, π/2>dt ∫ <0, 2cost> r^2 rdr
= ∫<-π/2, π/2>dt [r^4/4][ <0, 2cost>
= ∫<-π/2, π/2>4(cost)^4dt = 8∫<0, π/2>(cost)^4dt
= 2∫<0, π/2>(1+cos2t)^2dt
= 2∫<0, π/2>[1+2cos2t+(cos2t)^2]dt
= ∫<0, π/2>[3+4cos2t+cos4t]dt
= [3t+2sin2t + (1/4)sin4t]<0, π/2> = 3π/2
I = ∫<-π/2, π/2>dt ∫ <0, 2cost> r^2 rdr
= ∫<-π/2, π/2>dt [r^4/4][ <0, 2cost>
= ∫<-π/2, π/2>4(cost)^4dt = 8∫<0, π/2>(cost)^4dt
= 2∫<0, π/2>(1+cos2t)^2dt
= 2∫<0, π/2>[1+2cos2t+(cos2t)^2]dt
= ∫<0, π/2>[3+4cos2t+cos4t]dt
= [3t+2sin2t + (1/4)sin4t]<0, π/2> = 3π/2
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