用积分求面积的一题 Find the surface area of the planeFind the surface area of the plane x+2y+4z =16cut 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
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![用积分求面积的一题 Find the surface area of the planeFind the surface area of the plane x+2y+4z =16cut 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](/uploads/image/z/12590111-47-1.jpg?t=%E7%94%A8%E7%A7%AF%E5%88%86%E6%B1%82%E9%9D%A2%E7%A7%AF%E7%9A%84%E4%B8%80%E9%A2%98+Find+the+surface+area+of+the+planeFind+the+surface+area+of+the+plane+x%2B2y%2B4z+%3D16cut+off+by+x+%3D+0%2Cy+%3D+0+and+x%5E2+%2B+y%5E2+%3D+9%2Cwhere+x%2Cy%3E0.%E5%B0%B1%E6%98%AF+%E5%9C%A8%E7%AC%AC%E4%B8%80%E8%B1%A1%E9%99%90%E9%87%8C+%E6%B1%82%E8%A2%ABx%3D0%2Cy%3D0%2C%E5%92%8Cx%5E2%2By%5E2%3D9+%E5%88%87%E5%89%A9%E4%B8%8B%E7%9A%84%E9%82%A3%E9%83%A8%E5%88%86+x%2B2y%2B4z+%3D16%E5%B9%B3)
用积分求面积的一题 Find the surface area of the planeFind the surface area of the plane x+2y+4z =16cut 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
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?
用积分求面积的一题 Find the surface area of the planeFind the surface area of the plane x+2y+4z =16cut 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
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