8. Calculate the surface integral of the function G(x,y,z)=z-x over the surface given explicitly by graph of $z = x + y^2$ above the triangle in the xy plane with vertices (0,0,0), (1,1,0) and (0,1,0)
Added by Teresa J.
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Step 1: The surface is given by z = x + y², so we can write the surface integral as a double integral over the projection of the surface onto the xy-plane. Show more…
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15. Integrate G(x, y, z) = z - x over the portion of the graph of z = x + y2 above the triangle in the xy-plane having vertices (0, 0, 0), (1, 1, 0), and (0, 1, 0).
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Integrate $G(x, y, z)=z-x$ over the portion of the graph of $z=x+y^{2}$ above the triangle in the $x y$ -plane having vertices (0, 0,0)$,(1,1,0),$ and $(0,1,0) .$ (See accompanying figure.)
Integrals and Vector Fields
Surface Integrals
Integrate $G(x, y, z)=z-x$ over the portion of the graph of $z=x+y^{2}$ above the triangle in the $x y$ -plane having vertices $(0,0,0),(1,1,0),$ and $(0,1,0) .$ (See accompanying figure.) (FIGURE CAN'T COPY).
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