∫[L]x^2yzds其中为折线,这里A,B,C,D,依次为点(0,0,0),(0,0,2),(1,0,2),(1,3,2);

Question

∫[L]x^2yzds其中为折线,这里A,B,C,D,依次为点(0,0,0),(0,0,2),(1,0,2),(1,3,2);

Answer 1

∫[L]x^2yzds=∫[(0,0,0)->(0,0,2)] x^2yzds+∫[(0,0,2)->(1,0,2)] x^2yzds
+∫[(1,0,2)->(1,3,2)] x^2yzds
∫[(0,0,0)->(0,0,2)] x^2yzds=∫[0->2] 0dz=0
∫[(0,0,2)->(1,0,2)] x^2yzds=∫[0->1] x^2 * 0 *2dx=0
∫[(1,0,2)->(1,3,2)] x^2yzds=∫[0->3] 1^2 * y *2dy= y^2 | [0->3] = 9
∫[L]x^2yzds=0+0+9=9