This preview shows pages 1–4. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Sample problems on Chapter 14 Problem 1: Find the surface area of the torus T (shaped like a bagel) with surface described in parameterized form by x = (3 + cos t ) cos , y = (3 + cos t ) sin , z = sin t, where 0 t, 2 . Problem 2: Evaluate the line integral of cos x + sin y on the curve C : y = x, x / 2. Problem 3: Evaluate the integral of y over the surface S : z = cosh x, x 1 , y 1 . Problem 4: Find the work done by F = ( xy ) i + ( y ) j + ( yz ) k over the curve r ( t ) = t i + t 2 j + t k , 0 t 1. Problem 5: Let F = (2 y sin z ) j + ( y 2 cos z ) k represent a force field and consider a curved line C described by r ( t ) = t cos t 2 i + t sin t 2 j + t 2 k , 0 t p / 2. Calculate the work integral R C F d r by any legitimate means. Problem 6: Given the vector field F = ( y + 3) i + ( x z ) j + (sin z y ) k and the path described by two connected straight line segments from (0 , , 0) to (1 , 2 , 1) to (0 , , 1) a) Find a parameterization for a straight line segment from (0 , , 0) to (1 , 2 , 1)....
View
Full
Document
This test prep was uploaded on 09/23/2007 for the course MATH 1920 taught by Professor Pantano during the Fall '06 term at Cornell University (Engineering School).
 Fall '06
 PANTANO
 Multivariable Calculus

Click to edit the document details