Question

六道数学题，求助。

Answer 1

1、
①原式=∫(1,e)(1+lnx)d(lnx)
=[lnx+(1/2)*(lnx)^2]|(1,e)
=3/2
②原式=∫(0,-1)xd[e^(-x)]
=xe^(-x)|(0,-1)-∫(0,-1)e^(-x)dx
=-e+e^(-x)|(0,-1)
=-e+e-1
=-1
2、
①dz/dx=-y^2*sinx+9x^2*y
dz/dy=2ycosx+3x^3
所以dz=(-y^2*sinx+9x^2*y)dx+(2ycosx+3x^3)dy
②du/dx=-yz(1-xy)^(z-1)
du/dy=-xz(1-xy)^(z-1)
du/dz=ln(1-xy)*(1-xy)^z
所以du=[-yz(1-xy)^(z-1)]dx+[-xz(1-xy)^(z-1)]dy+[ln(1-xy)*(1-xy)^z]dz
3、这两小题最右边有部分照片没有拍全