2重积分|x|+|y|dxdy,|x|+|y_数学解答

2重积分|x|+|y|dxdy,|x|+|y

人气：451 ℃　时间：2020-06-07 16:12:19

解答

∫D∫|x|+|y|dS=4∫[0,1]∫[0,4-x](x+y)dxdy
=4∫[0,1]dx∫[0,4-x]d(xy+y^2/2)
=4∫[0,1](4-x)x+(1/2)(4-x)^2 dx
=4∫[0,1](-3/2)x^2-4x+8 dx
=2x^3-8x^2+32x |[0,1]
=2-8+32=24