20Chw7 - MATH 20C graded homework 7. (20 points) 15.3 #16...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: MATH 20C graded homework 7. (20 points) 15.3 #16 (10 points): Integrate f ( x,y,z ) = z over the region W below the upper hemisphere of radius 3 , but lying over the triangle in the xy-plane bounded by the lines x = 1 , y = 0 , and x = y . Solution: The region W is z-simple; it projects onto the region D (which may be taken as vertically or horizontally simple; both iterations are provided below). The sphere of radius 3 has equation x 2 + y 2 + z 2 = 9, and the top half has equation z = p 9- x 2- y 2 . Thus, each vertical line segment in W runs from z p 9- x 2- y 2 . The base D looks like .............................................................. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....
View Full Document

This note was uploaded on 03/28/2011 for the course MATH 20C taught by Professor Helton during the Winter '08 term at UCSD.

Page1 / 2

20Chw7 - MATH 20C graded homework 7. (20 points) 15.3 #16...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online