Machine-translated by Google. Questions are authored in English.
Top

Discussion

An integration over a region is to be carried out in the spherical system. The element of volume to be used is

  • A.\( r^2 \sin\theta \, dr \, d\theta \, d\phi \)
  • B.\( r \sin\theta \, dr \, d\theta \, d\phi \)
  • C.\( r^2 \, dr \, d\theta \, d\phi \)
  • D.\( r^2 \cos\theta \, dr \, d\theta \, d\phi \)

Answer: A

The two angular arc lengths are \( r \, d\theta \) and \( r \sin\theta \, d\phi \), and multiplying them by \( dr \) gives the element. Integrating it over the full ranges returns \( 4\pi r^3/3 \), which is the check worth remembering.

No comment is present. Be the first to comment.
Loading…

Post your comment

Please log in or register to post a comment.

Subject Categories

Examination Categories

About Us

ExamsRepo

Copyright © 2026 ExamsRepo . All Rights Reserved . With