2e^-(2x y)的二重积分-搜答案-智慧作业帮

原式=∫dy∫e^(-y²/2)dx(作积分顺序变换)=∫(1-y²)e^(-y²/2)dy=∫e^(-y²/2)dy-∫y²e^(-y²/

z＝xy/R.Zx′＝y/R.Zy′＝x/R.S＝∫∫[D]√（1+（y/R）²+（x/R）²）dxdyD:x²+y²≤R².用极坐标.S＝（1/R）

方程两边对x求导,得：y+xy'+y'e^y=2y+2xy'y'e^y-xy'=y得y'=y/(e^y-x)因此dy=ydx/(e^y-x)

答：做出图像,得y=e^(2x)在y=e^x上方.且在(0,1)处有交点.∫0到1dx∫e^x到e^(2x)dy=e^2/2-e+1/2

∫∫x^2e^(-y^2)dxdy=∫(0→1)e^(-y^2)dy∫(0→y)x^2dx=∫(0→1)e^(-y^2)*1/3*y^3dy=(1/3)∫(0→1)e^(-y^2)*y^2*(-1/2

对方程取导数y+x(dy/dx)+(dy/dx)=0(dy/dx)(x+1)=-ydy/dx=(-y)/(x+1)

∫dy∫e^(-x^2)dx=-∫dy∫e^(-x^2)dx=-∫dx∫e^(-x^2)dy=-∫e^(-x^2)dx∫dy=-∫xe^(-x^2)dx=1/2e^(-x^2)=1/2(e^(-1)-

∫(x=1→3)dx∫(y=x-1→2)e^(y²)dy交换积分次序：dydx→dxdyx=1到x=3,y=x-1到y=2y=0到y=2,x=1到x=y+1=∫(y=0→2)e^(y

交换积分次序：∫(0,2)dx∫(x,2)e^(-y²)dy=∫(0,2)dy∫(0,y)e^(-y²)dx=∫(0,2)ye^(-y²)dy=(1/2)∫(0,2)e^

∫e^(-x^2)dx=∫e^(-y^2)dy而∫e^(-x^2)dx*∫e^(-y^2)dy=∫∫e^(-y^2)*e^(-x^2)dxdy=∫∫e^(-x^2-y^2)dxdy然后是用极坐标换元,

楼上错了z=9-x^2-4y^2与xy平面围成的立体即z=9-x^2-4y^2>=0x^2+4y^2

∫∫xy²dxdy=∫dθ∫(rcosθ)*(rsinθ)²*rdr(应用极坐标变换)=∫(cosθsin²θ)dθ∫r^4dr=∫sin²θd(sinθ)∫r

你好!两边对x求导：e^(xy)*(y+xy')-y^2=y'cosy解得y'=(y^2-ye^(xy))/(xe^(xy)-cosy)

可以使用符号函数,比如：%Bylyqmathclc;clearall;closeall;symsxyeq=exp(x*y)-2*x*y;z=int(int(eq,x,1,0),y,-1,1);vpa(

经检验,无误

∫∫(D)(x²+y)dxdy=∫(1→2)dx∫(1/x→x)(x²+y)dy=∫(1→2)[x²y+y²/2]|(1/x→x)dx=∫(1→2)[x

y=x及y=2x,y=1交点(1/2,1),(1,1)则∫∫e^y^2dσ=∫[0,1]∫[y/2,y]e^y^2dxdy=∫[0,1]e^y^2∫[y/2,y]dxdy=∫[0,1]e^y^2*y/