用积分求面积的一题 Find the surface area of the plane
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用积分求面积的一题 Find the surface area of the plane
Find the surface area of the plane x+2y+4z =16
cut off by x = 0,y = 0 and x^2 + y^2 = 9,where x,y>0.
就是 在第一象限里 求被x=0,y=0,和x^2+y^2=9 切剩下的那部分
x+2y+4z =16平面的面积
形状大致像三角形被切了一块
应该用什么方法?双重积分?还是面积分?
如果用面积分 怎么设参数?
Find the surface area of the plane x+2y+4z =16
cut off by x = 0,y = 0 and x^2 + y^2 = 9,where x,y>0.
就是 在第一象限里 求被x=0,y=0,和x^2+y^2=9 切剩下的那部分
x+2y+4z =16平面的面积
形状大致像三角形被切了一块
应该用什么方法?双重积分?还是面积分?
如果用面积分 怎么设参数?
题目是:求平面 x+2y+4z =16被x = 0,y = 0 和x^2 + y^2 = 9所截的面积,这里x,y>0.
曲面方程为:z =(16-x-2y)/4,z'x=-1/4,z'y=-1/2
曲面在xoy平面的投影为D:x^2 + y^2 《 9,x,y>0
故:S=∫∫√(1+1/16+1/4)dxdy
=(√21)/4∫∫dxdy
=(√21)/4*(1/4)π*9
=9π(√21)/16
曲面方程为:z =(16-x-2y)/4,z'x=-1/4,z'y=-1/2
曲面在xoy平面的投影为D:x^2 + y^2 《 9,x,y>0
故:S=∫∫√(1+1/16+1/4)dxdy
=(√21)/4∫∫dxdy
=(√21)/4*(1/4)π*9
=9π(√21)/16
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