We can solve these equations together for z and x(we need two parameters):
z = y or z = -y & x = sqrt(1 - y^2) or x = -sqrt(1 - y^2) . The surface area can be formulized as (integral) z ds.
Here ds = sqrt (1 + (dx/dy)^2) dy. Since (dx/dy)^2 = (y^2) / (1 - y^2), we get ds = 1 / sqrt(1 -...
1. Homework Statement
Find the surface area of the region common to the intersecting cylinders
x^2 + y^2 = 1 and x^2 + z^2 = 1.
2. Homework Equations
3. The Attempt at a Solution
I know that the answer is 16 but why? How can we parametrize this surfaces?
The...
Okay, i got it. The normal to the plane is n=(1,0,-1) but we need an outward normal so we take n=(-1,0,1). We get (3,2,1)(-1,0,1) = -2. Projection onto xy-plane is a circle whose area is 4*Pi and multiplying it by -2 we obtain 8*Pi.
Homework Statement
Solve the following question by using Stokes' Theorem.
(Line integral on C) 2zdx + xdy + 3ydz = ? where C is the ellipse formed by
z = x, x^2 + y^2 = 4.
Homework Equations
The Attempt at a Solution
We have the vector A=(2z,x,3y) which is cont...