a) Let Fand let → (x, y, z) = (x, y, z) S be the surface given by z = 16 – x with and upward orientation. 2 – y 2 z 2 7 Compute S directly. Hint: the answer is S SF→· dS → 369n 2. b) Do the adaptation (the adding and subtracting) you mentioned above and find integral with divergence theorem. Note: you should get the same value as in part (a).

Q: For F(x, y, z) = x²z² i+ sinx z²j+zx²y*k, find div F and curl F.

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A: We will find line integral by using stokes theorem .

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A:

Q: Consider the following. C: counterclockwise around the circle  x2 + y2 = 49  from  (7, 0) to (−7, 0)…

A: Given,   C: Counterclockwise around the circle            x2+y2=49       from (7, 0), and (-7, 0).…

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A:

Q: 2) Find the work of F = (x² - y² -4,2xy) on the semi-circle of radius 2 centered at the origin…

A: ∮F·dr=∮x2-y2-4dx+2xydy             =∬S∂∂x2xy-∂∂yx2-y2-4 dxdy               By applying Greens…

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Q: Use Green's Theorem to evaluate the following line integral. Assume the curve is oriented…

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A: In this question, the concept of the equation of the tangent plane is applied. The Equation of…

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A: Given, the line integral Where C is the triangle with vertices.

Q: Given: Find (a) div F (b) curl F

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Q: F(x, y) = (x√x+y, a² + √y) and C is the circle x² + y² = 4 oriented counterclockwise What process…

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Q: 7. Let F(x, y,z)=-2yi +2xj. Use Stokes’ Theorem to find F dr where C is a circle (a) Parallel to the…

A: By stoke's theorem

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Q: =Fdx+F;dy is called exact if Fidr=vf.dr scalar function. For F, Fidr+ Fgdz ® F(x.y)=xi+ yi,…

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