The figure shows the surface created when the cylinder y2 + z2 = 1 intersects the cylinder x2 + z2 = 1. Find the area of this surface.
To find: The area of the given surface.
The surface area with equation , where and are continuous, is .
Here, D is the given region.
The surface is the cylinder intersects another cylinder .
Solve the given equations,
Since the given surface is the cylinder of radius 1, x ranges from 0 to 1 in the first quadrant of the xy-plane. So, the total area is 8 times the surface area of the above mentioned region in the first quadrant.
The partial derivatives and are,
Then, by the formula mentioned above, the area of the surface is given by,
Integrate it with respect to y and apply the limit
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