大师作文网利用格林公式计算
来源：学生作业帮 编辑：大师作文网作业帮 分类：数学作业 时间：2024/10/01 07:38:30
利用格林公式计算
I = ∮x^2ydx+y^2xdy =∫∫(y^2-x^2)dxdy
=∫dt∫r^2[(sint)^2-(cost)^2]rdr
=∫(-cos2t)dt[r^4/4]
=∫4(cost)^4(-cos2t)dt
= -2∫(1+cos2t)^2(cos2t)dt
= -2∫[cos2t+2(cos2t)^2+(cos2t)^3]dt
= -2∫(cos2t+1+cos4t)dt -∫[1-(sin2t)^2]dsin2t
= -2[t+sin2t/2+sin4t/4] - [sin2t-(sin2t)^3/3]
= -π
=∫dt∫r^2[(sint)^2-(cost)^2]rdr
=∫(-cos2t)dt[r^4/4]
=∫4(cost)^4(-cos2t)dt
= -2∫(1+cos2t)^2(cos2t)dt
= -2∫[cos2t+2(cos2t)^2+(cos2t)^3]dt
= -2∫(cos2t+1+cos4t)dt -∫[1-(sin2t)^2]dsin2t
= -2[t+sin2t/2+sin4t/4] - [sin2t-(sin2t)^3/3]
= -π