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Chapter 6: Q11P (page 335)

鈭�V鈭�苍诲蟽over the entire surface of a cube in the first octant with edges of length 2along the coordinate axes, whereV=(x2鈭�y2)i+3yj鈭�2xzk.

Short Answer

Expert verified

The solution derived isI=24.

Step by step solution

01

Given Information.

The given equation isV=(x2鈭�y2)i+3yj鈭�2xzk

02

Definition of vector.

A quantity that has magnitude as well as direction is called a vector. It is typically denoted by an arrow in which the head determines the direction of the vector and the length determines its magnitude.

03

Apply divergence theorem.

Apply the divergence theorem and the fact that 鈭�脳V=2x+3鈭�2x=3then the integral becomes as mentioned below.

I=3鈭�V鈥�诲蟿

=3脳8

=24

Hence, the solution derived is I=24..

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Most popular questions from this chapter

鈭�Cexcosydx-exsinydy, whereCis the broken line fromA=(ln2,0)to D=(0,1)and then from DtoB=(-ln2,0).

鈭�C鈥�(x2鈭�y)dx+(x+y3)dy: where Cis the parallelogram with vertices (0,0),(2,0),(1,1),(3,1).

鈭�(2xi鈭�2yj+5k)脳苍诲蟽over the surface of a sphere of radius 2and center at the origin.

(a) Suppose that a hill (as in Fig. 5.1) has the equation 32-x2-4y2, where z=heightmeasuredfromsomerefrencelevel(in hundreds of feet). Sketch acontour map (that is, draw on one graph a set of curvesz=const.); use the contours z=32,19,12,7,0(b) If you start at the point(3,2)and in the directioni+j, are you going up hillor downhill, and how fast?

鈭�C(yex-1)dx+exdy,where Cis the semicircle through(0,-10),(10,0),and(0,10)(Compare Problem 4.)
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