View the step-by-step solution to:


Suppose that S is the portion of the surface {z = 5 − x2 − y2} confined to the region {0 ≤ z ≤ 1}. Let F

= (h−2xy ,y ,3x). (a) Find the area of S. (b) Let n be the unit normal vector to S pointing in the positive z-direction. Calculate ZZS(curl F)·ndS . (c) Let E be the solid whose boundary is made of S capped off with the disk of radius 2 located at height z = 1 and with the disk of radius √5 located at height z = 0 (both disks have their center on the z-axis). Calculate ZZ∂E n·FdS , where n is the outer normal unit vector to E.

Recently Asked Questions

Why Join Course Hero?

Course Hero has all the homework and study help you need to succeed! We’ve got course-specific notes, study guides, and practice tests along with expert tutors.

  • -

    Study Documents

    Find the best study resources around, tagged to your specific courses. Share your own to gain free Course Hero access.

    Browse Documents
  • -

    Question & Answers

    Get one-on-one homework help from our expert tutors—available online 24/7. Ask your own questions or browse existing Q&A threads. Satisfaction guaranteed!

    Ask a Question
Ask Expert Tutors You can ask You can ask ( soon) You can ask (will expire )
Answers in as fast as 15 minutes