Question Solved1 Answer 14. Evaluate the line integral where v = (2yz + 3x2)i + (y2 + 4xz)j + (222 + 6xy)k and C is the curve with parametric equations x = tº, y = 62, z = t, joining the points (0,0,0) and (1,1,1).

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Transcribed Image Text: 14. Evaluate the line integral where v = (2yz + 3x2)i + (y2 + 4xz)j + (222 + 6xy)k and C is the curve with parametric equations x = tº, y = 62, z = t, joining the points (0,0,0) and (1,1,1).
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Transcribed Image Text: 14. Evaluate the line integral where v = (2yz + 3x2)i + (y2 + 4xz)j + (222 + 6xy)k and C is the curve with parametric equations x = tº, y = 62, z = t, joining the points (0,0,0) and (1,1,1).
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we have to evaluate{:[int_(c)v*dr", wher "c:r=x hat(i)+y hat(ȷ)+2 hat(u)"; "],[x=t^(3)+y=t^(2)","z=t],[" with "(0","0","0)","(1","1","1)],[" - Now, "dx=3t^(2)dt],[{:[dy=2tdt quadt^(')" change from oto1 "],[dt=dt]:}],[int_(c)v*dp=int_(c)^(1)(2yz+3x^(2))dx+(y^(2)+4xz)dy],[+(2z^(2)+6x)dz],[=int_(0)^(1)(2*t^(2)*t+3*t^(6))3t^(2)dt],[+(t^(4)+4*t^(3)*t)2tdt] ... See the full answer