practice final - Sample problems on Chapter 14 Problem 1:...

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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)....
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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).

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practice final - Sample problems on Chapter 14 Problem 1:...

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