Let m be the capped cylindrical surface which is the union of two surfaces, a cylinder given by x^2 + y^2 = 81,\ 0 \le z \le 1, and a hemispherical cap defined by x^2 + y^2 + (z-1)^2 = 81,\ z \ge 1. for the vector field \mathbf{f} = (zx + z^2y + 7 y,\ z^3yx + 2 x,\ z^4x^2), compute \iint_m (\nabla \times \mathbf{f}) \cdot d\mathbf{s} in any way you like.

answer: you need to organize this better it does not make sense.

step-by-step explanation: ?

answer: what are the answer choices?

step-by-step explanation:

the answer is:

the correct option is the option b.

to calculate the surface area of the right cylinder, we need to use the following formula:

from the picture we know that:

so, substituting and calculting we have:

hence, we have that the correct option is the option b.

have a nice day!