2220hw10 - Math 2220 Problem Set 10 Spring 2010 Section 6.1...

Info iconThis preview shows page 1. Sign up to view the full content.

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

Unformatted text preview: Math 2220 Problem Set 10 Spring 2010 Section 6.1 : 2. Calculate the integral of the function f ( x,y,z ) = xyz over the curve c ( t ) = ( t, 2 t, 3 t ), t 2. 4. Calculate the integral of f ( x,y,z ) = 3 x + xy + z 3 over the curve c ( t ) = (cos 4 t, sin4 t, 3 t ), t 2 . 8. Calculate integraltext C F d s for the vector field F ( x,y,z ) = ( x,y,- z ) where C is the curve c ( t ) = ( t, 3 t 2 , 2 t 3 ),- 1 t 1. 18. Evaluate integraltext C ( x 2- y ) dx +( x- y 2 ) dy where C is the line segment from (1 , 1) to (3 , 5). 22. Calculate integraltext C z dx + xdy + y dz where C is the curve obtained by intersecting the surfaces z = x 2 and x 2 + y 2 = 4, and C is oriented counterclockwise when viewed from above. 28. Let F be the radial vector field F = x i + y j + z k . Show that integraltext C F d s = 0 whenever C is a curve c ( t ) = ( x ( t ) ,y ( t ) ,z ( t )) that lies on the sphere x 2 + y 2 + z 2 = c 2 . Hint: Differentiate [ x ( t )] 2 + [ y ( t )] 2 + [...
View Full Document

This note was uploaded on 04/21/2010 for the course MATH 2220 taught by Professor Parkinson during the Spring '08 term at Cornell University (Engineering School).

Ask a homework question - tutors are online