Question

Let C be a closed curve parametrized by r(t) = sin ti+cos tj with 0 ≤...

Let C be a closed curve parametrized by r(t) = sin ti+cos tj with 0 ≤ t ≤ 2π. Let F = yi − xj be a vector field.

(a) Evaluate the line integral xyds. C

(b) Find the circulation of F over C. (c) Find the flux of F over C.

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
Let C be the curve parametrized by r(t)=(t2+2)i+(1+t)j+2t^2k, with 0≤t≤. Consider the conservative vector field F=yz2i+xz2j+2xyzk,...
Let C be the curve parametrized by r(t)=(t2+2)i+(1+t)j+2t^2k, with 0≤t≤. Consider the conservative vector field F=yz2i+xz2j+2xyzk, Calculate ∫CF⋅dr
(a) Is the vector field F = <e^(−x) cos y, e^(−x) sin y> conservative? (b) If...
(a) Is the vector field F = <e^(−x) cos y, e^(−x) sin y> conservative? (b) If so, find the associated potential function φ. (c) Evaluate Integral C F*dr, where C is the straight line path from (0, 0) to (2π, 2π). (d) Write the expression for the line integral as a single integral without using the fundamental theorem of calculus.
6.) Let ~r(t) =< 3 cos t, -2 sin t > for 0 < t <...
6.) Let ~r(t) =< 3 cos t, -2 sin t > for 0 < t < pi. a) Sketch the curve. Make sure to pay attention to the parameter domain, and indicate the orientation of the curve on your graph. b) Compute vector tangent to the curve for t = pi/4, and sketch this vector on the graph.
With the parametric equation x=cos(t)+tsin(t), y=sin(t)-tcos(t) , 0 ≤ t ≤ 2π) Find the length of...
With the parametric equation x=cos(t)+tsin(t), y=sin(t)-tcos(t) , 0 ≤ t ≤ 2π) Find the length of the given curve. (10 point)     2) In the circle of r = 6, the area above the r = 3 cos (θ) line Write the integral or integrals expressing the area of ​​this region by drawing. (10 point)
Let F (x, y) = 2xyi + (x – 2y)j, r (t) = sin ti –...
Let F (x, y) = 2xyi + (x – 2y)j, r (t) = sin ti – 2 cos t j, 0 ≤ t ≤ π. Then C F•dr is
Problem 7. Consider the line integral Z C y sin x dx − cos x dy....
Problem 7. Consider the line integral Z C y sin x dx − cos x dy. a. Evaluate the line integral, assuming C is the line segment from (0, 1) to (π, −1). b. Show that the vector field F = <y sin x, − cos x> is conservative, and find a potential function V (x, y). c. Evaluate the line integral where C is any path from (π, −1) to (0, 1).
Evaluate C (y + 6 sin(x)) dx + (z2 + 2 cos(y)) dy + x3 dz...
Evaluate C (y + 6 sin(x)) dx + (z2 + 2 cos(y)) dy + x3 dz where C is the curve r(t) = sin(t), cos(t), sin(2t) , 0 ≤ t ≤ 2π. (Hint: Observe that C lies on the surface z = 2xy.) C F · dr =
Let ? (?, ?) = (? 2 cos ? + cos ?)? + (2? sin ?...
Let ? (?, ?) = (? 2 cos ? + cos ?)? + (2? sin ? − ? sin ?)? . a. Show that ?⃗ is conservative and find a potential function f such that ∇? = ?⃗ b. Evaluate ∫ ? ∙ ?? ? where C is the line segment from (0, ?/4 ) to ( ?/6 , ?/2 )
Given vector field ?⃗ =< −?, ?? > on the curve C given ?⃗(?) =< 3...
Given vector field ?⃗ =< −?, ?? > on the curve C given ?⃗(?) =< 3 cos ?, 3 sin ? > for 0 ≤ ? ≤ 2? a. Determine the circulation of ?⃗ on C b. Determine the flux of ?⃗ on C
Question(9) Curve ? = t - sin t, y = 1 - cos t, 0 ≤...
Question(9) Curve ? = t - sin t, y = 1 - cos t, 0 ≤ ? ≤ 2? given. a) Take the derivatives of x and y according to t and arrange them. b) Write and edit the integral that gives the surface area of the object formed by rotating the given curve around the x axis. c) Solve the integral and find the surface area.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT