多重积分的MATLAB实现

1、2Mg1.学习MATLAB2.利用MATLAB1.intint(int(f,y,y1(x),y2(x),x,a,b)int(int(int(f,z,z1(x,y),z2(x,y),y,y1(x),y2(x),x,a,b)2.dblquad(fun,xmin,xmax,ymin,ymax)triplequad(fun,xmin,xmax,ymin,ymax,zmin,zmax)quadl1.y2-x)dxdyy=2,y=x及y=2x222dyy(x2y2x)dxoy2int(int(x2果ans=13x,x,y/2,y),y,0,2)2221sinx1dydxyx22int(int(sin(x)

2、/x,x,yanspi,pi),y,pi,2*pi)Mg3sin(X2+y2)dxdyX2+y211,1X2y1X2,1XMx1X2sin(x2+y2)dy,-1-1-X2t(1-xA2),x,-1,1)matlab求不出int(int(sin(pi*(x人2+y人2),y,-sqt(1-x人2),sq由输出结果可以看出,结果中仍带有int,表2da1sin(2)d,int(int(*sin(pi*人2),0,l),a,0,2*pi)结果为ans=2.4MxMydxdy=(x，y)|0 x1,1y2symsxy;%a=int(int(xAy,x,0,1),y,1,2)%a=log(3)-log

3、(2)b=simple(a)%b=log(3/2)c=vpa(b,4)%c=0.4055例5(P3651.(1)fun=inline(x.A3+3.*x.A2.*y+y.A3,x,y);dblquad(fun,0,1,0,1)ans=1.0000例6(P3651.(2)fun=inline(sin(x+y),x,y);dblquad(fun,0,pi/2,0,pi/2)ans=2.0000P3651.(3)fun=inline(x+y).*exp(x+y),x,y);dblquad(fun,0,1,2,4)ans=Mg315.95762.三重例8dx00 xdy10 xy_(1dzx+yz)3

4、n(n(n(1(1xyz)3,z,0,lxy),y,O,lx),x,O,l)ans=-5/16+1/2*log(2)xyzdxdydzX2y2z2=11dx1x2dy1x2y2xyzdz000n(n(n(z*y,*qr(1x2y2),y,0,sqr(1x2),x,0,l)ans=1/48例10(P3831.(1)xy2Z2dxdydzz=xyy=xx=1z=0所围成。quadl(x)arrayfun(xx)quadl(y)arrayfun(yy)quadl(z)xx.*yy.*z,xx*yy,2*xx*yy),y),xx,2*xx),x),1,2)ans=179.2969quadl(x)arrayfun(xx)quadl(y)arrayfun(yy)quadl(z)xx.*yy.*z,xx*yy,2*xx*yy),y),xx,2*xx),x),1,2)ans=179.2969注：1课本上的三重积分都可以用这种方法计算：将三重积分化成三quadl即可，其用法为：quadl(x)arrayfun(xx)quadl(y)arrayfun(yy)quadl(被积函数f(xx,yy,z)关于z变量的函数句柄,z积分下z1(xx,yy)