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Chapter 14: Q. 44 (page 1120)

Find

鈭�S鈥�F(x,y,z)鈰�ndSifF(x,y,z)=ln鈦�x2+y2+1z+3i+yy+1j+ez2k

Where S is the portion of the sphere with radius 2, centered at the origin, and that lies below the plane with equation z=-2, with n pointing outwards.

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Step by step solution

01

Step 1. Given information.

given, F(x,y,z)=ln鈦�x2+y2+1z+3i+yy+1j+ez2k

02

Step 2. 

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Most popular questions from this chapter

F(x,y,z)=i+j+k, where S is the lower half of the unit sphere, with n pointing outwards.

ComputethecurlofthevectorfieldsinExercises23鈥�28.F(x,y,z)=xeyzi+yexzj+zexyk

Use what you know about averages to propose a formula for the average rate of flux of a vector field F(x, y ,z) through a smooth surface S in the direction of n.

Use the curl form of Green鈥檚 Theorem to write the line integral of F(x, y) about the unit circle as a double integral. Do not evaluate the integral.

Integrate the given function over the accompanying surface in Exercises 27鈥�34.
f(x,y,z)=xyz2, where S is the portion of the cone 3z=x2+y2 that lies within the sphere of radius 4 and centered at the origin.
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