Question

Consider the integral of f(x, y, z) = z + 1 over the upper hemisphere σ:...

Consider the integral of f(x, y, z) = z + 1 over the upper hemisphere σ: z = 1 − x2 − y2 (0 ≤ x2 + y2 ≤ 1). (a) Explain why evaluating this surface integral using (8) results in an improper integral. (b) Use (8) to evaluate the integral of f over the surface σr : z = 1 − x2 − y2 (0 ≤ x2 + y2 ≤ r2 < 1). Take the limit of this result as r →1− to determine the integral of f over σ. (c) Parametrize σ using spherical coordinates and evaluate the integral of f over σ using (6). Verify that your answer agrees with the result in part (b).

Math   Advanced-Math   
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
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 ∫∫Sf(x,y,z)dS , where f(x,y,z)=0.4sqrt(x2+y2+z2)) and S is the hemisphere x2+y2+z2=36,z≥0
Evaluate ∫∫Sf(x,y,z)dS , where f(x,y,z)=0.4sqrt(x2+y2+z2)) and S is the hemisphere x2+y2+z2=36,z≥0
Evaluate the surface integral (double integral) over S: G(x,y,z) d sigma using a parametric description of...
Evaluate the surface integral (double integral) over S: G(x,y,z) d sigma using a parametric description of the surface. G(x,y,z)= 3z^2, over the hemisphere x^2+y^2+z^2=16, with z greater than or equal to 0.
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
Use spherical coordinates to calculate the triple integral of ?(?, ?, ?)=?f(x, y, z)=y over the...
Use spherical coordinates to calculate the triple integral of ?(?, ?, ?)=?f(x, y, z)=y over the region ?^2+?^2+?^2≤10, ∫∫∫?? ??=
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=
Evaluate the flux integral ∫ ∫ S F · n dS. F = 〈8, 0, z〉,...
Evaluate the flux integral ∫ ∫ S F · n dS. F = 〈8, 0, z〉, S is the boundary of the region bounded above by z = 25 − x2 − y2 and below by z = 1 (n outward). Enter an exact answer. Do not use decimal approximations.
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.
Quesiton: Compute the surface integral of f(x,y,z)=x^2 over z=sqrt(x^2+y^2), 0<=z<=1.
Quesiton: Compute the surface integral of f(x,y,z)=x^2 over z=sqrt(x^2+y^2), 0<=z<=1.
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
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT