Mathematics, 19.08.2020 01:01, ghadeeraljelawy
Evaluate the line integral ∫CF⋅dr, where F(x, y,z)=−xi−2yj−zk and C is given by the vector function r(t)=⟨sint, cost, t⟩, 0≤t≤3π/2.
Answers: 2
![= \int^{3 \pi/2}_0 \ [3 sin \ t \ cos \ t - 1 \ t ] \ dt](/tpl/images/0724/3126/fc962.png)
![= 3 [ \dfrac{u^2}{2}]^{3 \pi/2}_0 - 1 [ \dfrac{t^2}{2}]^{3 \pi/2}_0](/tpl/images/0724/3126/d2fe7.png)
![= \dfrac{3}{2} [ cos ^2 \ t ] ^{3 \pi/2} _0- \dfrac{1}{2} ( \dfrac{ 3 \pi }{2 })^2 - 0^2](/tpl/images/0724/3126/90b2a.png)
![= \dfrac{3}{2} [ cos ^2 \ \dfrac{3 \pi}{2} - cos ^2 \ 0 ] - \dfrac{1}{2}( \dfrac{9 \pi^2}{4})](/tpl/images/0724/3126/20a8b.png)
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Evaluate the line integral ∫CF⋅dr, where F(x, y,z)=−xi−2yj−zk and C is given by the vector function...
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