The surface integral where is the part of the plane which lies inside the cylinder is which of the following?
D) 0
E) None of the answers is correct.

Question

The surface integral  where  is the part of the plane  which lies inside the cylinder  is which of the following?
D) 0 
E) None of the answers is correct.

Quizplus · Accepted Answer

Since the plane 11eaa655_3a8c_85a6_a696_835ba583a266_TB5596_11 is completely inside the cylinder 11eaa655_3a8c_85a7_a696_2f43c3316f18_TB5596_11, the intersection of the plane and the cylinder is the entire plane. Therefore, the surface integral over the plane is just the integral of the constant function 1 over the plane, which gives the area of the plane. Since the plane has zero height, its area is zero, so the surface integral is also zero.

The Surface Integral Where Is the Part of the Plane