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Evaluate the Line Integral Along the Curve C A) π4\frac { \pi } { 4 }

question 134

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Evaluate the line integral along the curve C.
- C1x2+y2+z2ds,C is the path given by: C1:r(t) =(2cost) i+(2sint) j from (2,0,0)  to (0,2,0) C2:r(t) =(2sint) j+(2cost) k from (0,2,0)  to (0,0,2) C3:r(t) =(2sint) i+(2cost) k from (0,0,2)  to (2,0,0) \begin{array} { l } \int _ { C } \frac { 1 } { x ^ { 2 } + y ^ { 2 } + z ^ { 2 } } d s , C \text { is the path given by: } \\C _ { 1 } : \mathbf { r } ( t ) = ( 2 \cos t ) \mathbf { i } + ( 2 \sin t ) \mathbf { j } \text { from } ( 2,0,0 ) \text { to } ( 0,2,0 ) \\C _ { 2 } : \mathbf { r } ( t ) = ( 2 \sin t ) \mathbf { j } + ( 2 \cos t ) \mathbf { k } \text { from } ( 0,2,0 ) \text { to } ( 0,0,2 ) \\C _ { 3 } : \mathbf { r } ( t ) = ( 2 \sin t ) \mathbf { i } + ( 2 \cos t ) \mathbf { k } \text { from } ( 0,0,2 ) \text { to } ( 2,0,0 ) \end{array}

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