Question

Evaluate surface integral of double integral of Z dS, where S is the surface x = y+2z^2, 0 14 years ago

Answer 1

this is a weird shape, but since we are integrating over a rectangle I think it should be ok

Answer 2

oh help me pls i'm so lost about this surface integrals business.

Answer 3

the surface is\[g(y,z)=x=y+2z^2\]so we can now use the formulas for a surface integral\[\int\limits_S\int f(x,y,z)dS=\int\limits_D\int f(g(y,z),y,z)\sqrt{(g_y)^2+(g_z)^2+1}dA\]where D is the rectangle in the yz-plane