Question

Calculate the line integral of the vector field ?=〈?,?,?2+?2〉F=〈y,x,x2+y2〉 around the boundary curve, the curl of...

Calculate the line integral of the vector field ?=〈?,?,?2+?2〉F=〈y,x,x2+y2〉 around the boundary curve, the curl of the vector field, and the surface integral of the curl of the vector field.

The surface S is the upper hemisphere

?2+?2+?2=36, ?≥0x2+y2+z2=36, z≥0

oriented with an upward‑pointing normal.

(Use symbolic notation and fractions where needed.)

∫?⋅??=∫CF⋅dr=

curl(?)=curl(F)=

∬curl(?)⋅??=∬Scurl(F)⋅dS=

Math   Calculus   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Evaluate the surface integral S F · dS for the given vector field F and the...
Evaluate the surface integral S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = yi − xj + 2zk, S is the hemisphere x2 + y2 + z2 = 4, z ≥ 0, oriented downward
Compute the surface integral over the given oriented surface: F=〈0,9,x2〉F=〈0,9,x2〉 ,  hemisphere x2+y2+z2=4x2+y2+z2=4, z≥0z≥0 ,  outward-pointing normal
Compute the surface integral over the given oriented surface: F=〈0,9,x2〉F=〈0,9,x2〉 ,  hemisphere x2+y2+z2=4x2+y2+z2=4, z≥0z≥0 ,  outward-pointing normal
Evaluate the surface integral F · dS for the given vector field F and the oriented...
Evaluate the surface integral F · dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = x2 i + y2 j + z2 k S is the boundary of the solid half-cylinder 0 ≤ z ≤ 4 − y2 , 0 ≤ x ≤ 5
Evaluate the surface integral S F · dS for the given vector field F and the...
Evaluate the surface integral S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = x2 i + y2 j + z2 k S is the boundary of the solid half-cylinder 0 ≤ z ≤ 25 − y2 , 0 ≤ x ≤ 3
Evaluate the surface integral ∫∫S F · dS for the given vector field F and the...
Evaluate the surface integral ∫∫S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = xz i + x j + y k S is the hemisphere x2 + y2 + z2 = 4, y ≥ 0, oriented in the direction of the positive y-axis. Incorrect: Your answer is incorrect.
Evaluate the surface integral S F · dS for the given vector field F and the...
Evaluate the surface integral S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = yi − xj + 4zk, S is the hemisphere x^2 + y2^ + z^2 = 4, z ≥ 0, oriented downward
Evaluate the surface integral Evaluate the surface integral S F · dS for the given vector...
Evaluate the surface integral Evaluate the surface integral S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = x i + y j + 9 k S is the boundary of the region enclosed by the cylinder x2 + z2 = 1 and the planes y = 0 and x + y =...
Evaluate the surface integral    S F · dS for the given vector field F and...
Evaluate the surface integral    S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = x i − z j + y k S is the part of the sphere x2 + y2 + z2 = 4 in the first octant, with orientation toward the origin
Evaluate the surface integral S F · dS for the given vector field F and the...
Evaluate the surface integral S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = x i − z j + y k S is the part of the sphere x2 + y2 + z2 = 25 in the first octant, with orientation toward the origin
Evaluate the surface integral ∫∫S F · dS for the given vector field F and the...
Evaluate the surface integral ∫∫S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = x i - z j + y k S is the part of the sphere x2 + y2 + z2 = 81 in the first octant, with orientation toward the origin.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT