Home / Expert Answers / Advanced Math / direction-10-use-the-divergence-theorem-to-evaluate-the-surface-integral-ff-f-ds-where-f-zi-2yz-pa623

(Solved): direction. 10. Use the Divergence Theorem to evaluate the surface integral ff, F-ds where F zi + 2yz ...



direction. 10. Use the Divergence Theorem to evaluate the surface integral ff, F-ds where F zi + 2yzj - ryk, and the closed surface S is comprised of the √4x²-y² in octents one and two and the planes part of the sphere z = y = 0, z = 0.

10. Use the Divergence Theorem to evaluate the surface integral \( \iint_{S} \mathbf{F} \cdot d s \) where \( \mathbf{F}=z \m
10. Use the Divergence Theorem to evaluate the surface integral where . and the closed surface is comprised of the part of the sphere in octents one and two and the planes .


We have an Answer from Expert

View Expert Answer

Expert Answer



Step1
Applying the Divergence Theorem, we have: ? S F?ds = ? V div(F)dV where V is the region enclosed by the surface S. First, let's find the divergence of F: div(F) = ? ?x (zi) + ? ?y (2yzj) + ? ?z (-xyk) = 0 + 2z + 0 = 2z Now, we need to determine the limits for the triple integral. The surface S is comprised of the following parts:
We have an Answer from Expert

Buy This Answer $5

Place Order

We Provide Services Across The Globe