Test4Review - Test 4 Review 1. Find the length of the curve...

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Unformatted text preview: Test 4 Review 1. Find the length of the curve r ( t ) = (cos 3 t ) i + (sin 3 t ) k , t / 2. 2. A wire is given by the straight-line segment connecting (0 , 1 , 0) to (1 , , 0) and has density = x + y . Find the mass of the wire. 3. Calculate the work done by the force F = h 3 x 2- 3 x, 3 z, 1 i from (0 , , 0) to (1 , 1 , 1) over the path r ( t ) = h t, t 2 , t 4 i , t 1. 4. Let F = sin y cos x i +cos y sin x j + k . Show that F is conservative and find a potential function. Calculate the integral Z C sin y cos xdx + cos y sin xdy + dz where C is the straight-line from (1 , , 0) to (0 , 1 , 1). 5. Use Greens Theorem to evaluate I (6 y + x ) dx + ( y + 2 x ) dy where C is the (counter-clockwise) circle ( x- 2) 2 + ( y- 3) 2 = 4. 6. Find the area of the surface x 2- 2 y- 2 z = 0 that lies above the triangle bounded by the lines x = 2 , y = , y = 3 x in the xy-plane....
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