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15_4_9 - 9 Observe that if = e x y sin(y z then = e x y...

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9. Observe that if φ = e x + y sin ( y + z ) , then φ = e x + y sin ( y + z ) i + e x + y ( sin ( y + z ) + cos ( y + z ) ) j + e x + y cos ( y + z ) k . Thus, for any piecewise smooth path from ( 0 , 0 , 0 ) to ( 1 , π 4 , π 4 ) , we have Z e x + y sin ( y + z ) dx + e x + y ( sin ( y + z ) + cos ( y + z ) ) dy + e x + y cos ( y + z ) dz
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