evaluate the line integral ∫cf⋅dr, where f(x, y,z)=5xi−yj+zk and c is given by the vector function r(t)=⟨sint, cost, t⟩, 0≤t≤3π/2.

We have

and

so the line integral is equilvalent to

hope it you

step-by-step explanation:

sin(7pi/6 - pi/3)  

= sin(7pi/6 - 2pi/6)  

= sin(5pi/6)  

= sin(pi - pi/6)  

= sin(pi/6)  

= 1/2  

sin 7pi/6 - sin pi/3  

= sin (pi + pi/6) - sin pi/3  

= -sin pi/6 - sin pi/3  

= -1/2 - sqrt(3)/2  

= -(1+sqrt(3))2