Evaluate the line integral
β«π(π₯, π¦, π§) Γ β π ,
where π(π₯, π¦, π§) = (π¦^2 , π₯, π§) and the curve πͺ is described by π = π¦ = π π₯ with π₯ β [0,1].Β
parameter for of C,
x=t, y=etΒ ,z=etΒ .
r(t)=t i+ etΒ j+etΒ k
=> dr=(i + etΒ j + etΒ k)dt
Then,
"\\int_0^1 u.dr\\\\\n=\\int_0^1 (e^{2t},t,e^{t}).(1,e^t,e^t)dt\\\\\n=\\int_0^1 (2e^{2t}+te^{t})dt\\\\\n=[ e^{2t}+te^{t}-e^t]_0^1\\\\\n=e^2+e-e-1-0+1\\\\\n=e^2"
Comments
Leave a comment