VC4.6
From Exampleproblems
Let the given curve be C and let A(0,1,1) and B(1,0,1)be two points on curve C.
Therefore,![\int_{C} F\cdot\,dr=\int_{A}^{B} [(2x+yz)i+xzj+(xy+2z)k]\cdot(dxi+dyj+dzk)\,](/wiki/images/math/9/3/d/93d82f5cdd07272f640e2e913f9b0090.png)
=![\int_{A}^{B} [(2x+yz)dx+xzdy+(xy+2z)dz]\,](/wiki/images/math/2/c/8/2c8f05f91eb4c55ea7d052555bb7c4d4.png)
--(1)
While moving from A to B on the curve C,x varies from 0 to 1,y varies from 1 to 0 and z remains constant.Since z=1,so dz=0.Hence (1) reduces to
=![\int_{0}^{1} [2x+\sqrt{1-x^2}]dx-\int_{0}^{1}\sqrt{1-y^2} dy\,](/wiki/images/math/1/1/9/11907c46e0d559edb11102cc4fbeadc8.png)
=![2\int_{0}^{1} xdx+\int_{0}^{1}\sqrt{(1-x^2)}dx-\int_{0}^{1}\sqrt{(1-x^2)}dx=2[\frac{x^2}{2}]_{0}^{1}=1\,](/wiki/images/math/9/e/f/9efd09303a98531190df778635d1403c.png)
