calc_tutorial_16_5_006

 
Problem Statement

{6,12,18}
{2,3,4}
18/2
18/3
9*18
6*pow(18,2)
162/3
1944/2
1944+1
972*pow(4,2)-54*pow(4,3)

Compute for the given oriented surface.

F = <ez, z, x>, G(r, s) = (rs, r + s, r), 0 ≤ r ≤ 18, 0 ≤ s ≤ 4, oriented by Tr × Ts

 
Step 1

Question Sequence

Question 1

Recall how to find vector surface integrals. Let F be a vector field. Let G(u, v) be an oriented parametrization of an oriented surface S with parameter domain D. Assume that G is one-to-one and regular, except possibly at points on the boundary of D. Choose the correct integration for

A.
B.
C.

If the orientation of S is reversed, the surface integral changes sign.

Find Tr and Ts for G(r, s) = (rs, r + s, r). Then use these vectors to compute n(r, s).

Tr = (∂G / ∂r)

= <, , >

Ts = (∂G / ∂s)

= <, , >

n(r, s) = Tr × Ts

= <, , >

Correct.
Incorrect.

 
Step 2

Question Sequence

Question 2

Compute F(G(r, s)) given that F = <ez, z, x> and G(r, s) = (rs, r + s, r).

F(G(r, s)) =

A.
B.
C.
D.
Correct.
Incorrect.

 
Step 3

Question Sequence

Question 3

Compute the dot product F(G(r, s)) · n(r, s).

F(G(r, s)) · n(r, s) =<er, r, rs> · <-1, r, s - r > =

A.
B.
C.
D.
Correct.
Incorrect.

 
Step 4

Question Sequence

Question 4

Compute using the restrictions 0 ≤ r ≤ 18 and 0 ≤ s ≤ 4. Since we are orienting by Tr × Ts, which is the normal vector we found in Step 1, we need to change the sign of the integral.

= ( - e18) -

Correct.
Incorrect.