来自刘永立的问题
【计算二重积分:xsin(x+y)dσ,D:0≤x≤π,0≤y≤π/2急,希望详细一点,谢谢!】
计算二重积分:xsin(x+y)dσ,D:0≤x≤π,0≤y≤π/2
急,希望详细一点,谢谢!
1回答
2020-10-13 00:40
【计算二重积分:xsin(x+y)dσ,D:0≤x≤π,0≤y≤π/2急,希望详细一点,谢谢!】
计算二重积分:xsin(x+y)dσ,D:0≤x≤π,0≤y≤π/2
急,希望详细一点,谢谢!
两重积分先积sin(x+y)dy
IIxsin(x+y)dσ=IxdxIsin(x+y)dy
=IxdxIsin(x+y)d(x+y)
=Ixdx(-cos(x+y)):pi/2-0
=Ixdx(-cos(x+pi/2)+cos(x))
=Ixcos(x)dx-Ixcos(x+pi./2)dx
=(xsinx-Isinxdx)-I(x+pi/2)cos(x+pi/2)dx+pi/2*Icos(x+pi/2)dx
=cosx-(x+pi/2)sin(x+pi/2)-cos(x+pi/2)+pi/2*sin(x+pi/2):pi-0
=-2-(-3pi/2-pi/2)-0+pi/2*-2
=-2+2pi-pi
=pi-2