5. Evaluate the integral c. Work done by the force on a particle moving along the path C, F (x, y, z) = <x, y, -5z> C: r(t) = <2 cos t, 2 sin t, t>, 0 ? t ? 2? d. the work done where F = <y^3 +1, 3xy^2 +1>, and C is the semicircular path from (0,0) to (4, 0).
Added by Lori R.
Close
Step 1
First, we need to find the derivative of the given path, r(t) = <2 cos t, 2 sin t, t>. Show more…
Show all steps
Your feedback will help us improve your experience
Zack A and 78 other Calculus 3 educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Evaluate the integral Work done by the force on a particle moving along the path C, F (x, y, z) = <x, y, 2> C: r(t) = <2 cos t, 2 sin t, t>,
Madhur L.
Show that the integral: ∫(1,1,1) to (2,2,2) (x + 2y + 5z) dx + (2x - y + 3z) dy + (5x + 3y - 2z) dz is independent of path, and evaluate it.
Evaluate the work done by the force: F(x, y, z) = sin(x^2)i + cos(y^2)j + z^2k on a particle moved along the path: r(t) = cos(2t)i + sin(2t)j + 4k 0 ≤ t ≤ n
Sri K.
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD