If C is a piecewise smooth curve from (1,2,3) to (4,5,6), then ∫Cdx+2dy+3dz=?

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avortarF · Accepted Answer

Step 1  The value of the given function can be found with the help of the integration.  Substitution of limits in the respective variables helps to find the required values.  If a curve moves from (a,b,c) to the point (d,e,f), then the limit of the x varies from a to d, the limit of y varies from b to e, and the limit of z  varies from c to f.  Integration of the constant number is the constant multiple of the respective variable.  Step 2  Integrate the function with respect to the derivatives.  Integrate 1 with respect to x, since the derivatives available there is dx.  Integrate 2 with respect to y, since the derivatives available there is dy.  Integrate 1 with respect to z, since the derivatives available there is dz.  Substitute the limits of the curve in equation (1) with the help of the above procedure.  ∫Cdx+2dy+3dz=(1.x+2.y+3.z)C  =(x+2y+3z)C...(1)  =(4+2*5+3*6)-(1*1+2*2+3*3)  =32-14  =18

If C is a piecewise smooth curve from (1,2,3) to (4,5,6),then [SK\int_{C}dx+2dy+3dz=?

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