15 Evaluate F. dS, where F is the vector field x²i + 2zj – yk, over the curved surface S defined by x² + y² = 25 and bounded by z = 0, z = 6, y 2 3. %3D 16. A region V is defined by the quarterenh

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Chapter2: Second-order Linear Odes
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Solve this calclusQuestion 15.

3, x = 0, y = 0.
Us över the stated curved surface.
15 Evaluate F. dS, where F is the vector field x²i +2zj - yk, over the curved
surface S defined by x² + y = 25 and bounded by z = 0, z = 6, y 2 3.
%3D
16. A region V is defined by the quartersphere x2 + y2 + z? = 16, z 2 0, y 2 0 and
the planes z = 0, y = 0. A vector field F = xyi +y²j+k exists throughout and
on the boundary of the region. Verify the Gauss divergence theorem for the
region stated.
17 A surface consists of parts of the planes x = 0, x = 1, y = 0, y = 2, z = 1 in the
first octant. If F = yi + x²zj + xyk, verify Stokes' theorem.
18 Sis the surface z = x² + y² bounded by the planes z = 0 and z = 4. Verify Stokes'
theorem for a vector field F = xyi +x'j+ xzk.
%3D
%3D
Transcribed Image Text:3, x = 0, y = 0. Us över the stated curved surface. 15 Evaluate F. dS, where F is the vector field x²i +2zj - yk, over the curved surface S defined by x² + y = 25 and bounded by z = 0, z = 6, y 2 3. %3D 16. A region V is defined by the quartersphere x2 + y2 + z? = 16, z 2 0, y 2 0 and the planes z = 0, y = 0. A vector field F = xyi +y²j+k exists throughout and on the boundary of the region. Verify the Gauss divergence theorem for the region stated. 17 A surface consists of parts of the planes x = 0, x = 1, y = 0, y = 2, z = 1 in the first octant. If F = yi + x²zj + xyk, verify Stokes' theorem. 18 Sis the surface z = x² + y² bounded by the planes z = 0 and z = 4. Verify Stokes' theorem for a vector field F = xyi +x'j+ xzk. %3D %3D
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