Use a parametrization to express the area of the surface s as a double integral. then, evaluate the integral to find the area of the surface. s is the portion of the plane y + 3 z = 2 inside the cylinder x^2 + y^2 = 1.
Accepted Solution
A:
The cylinder gives you a hint as to where to start with a parameterization [tex]\mathbf s(u,v)=\langle x(u,v),y(u,v),z(u,v)\rangle[/tex]. A sensible choice would be to set
[tex]x=u\cos v[/tex] [tex]y=u\sin v[/tex]
so that
[tex]y+3z=2\implies z=\dfrac{2-u\sin v}3[/tex]
with [tex]0\le u\le1[/tex] and [tex]0\le v\le2\pi[/tex]. Then