Question

find surface area of the region to the common intersecting cylinder x^2+y^2=a^2 and x^2+z^2=a^2​

Answer 1

Answer:

the surface area common to the two cylinders x2+y2=a2 and x2+z2=a2 using surface integrals essentially.

My attempt: Let surface area = S and n^=∇(x2+y2)=1a(xi^+yj^)

S=∫∫ds=∫∫dydz|n^⋅i^|

=∫∫axdydz

=∫∫aa2−y2−−−−−−√dydz