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Unformatted text preview: ables to cylindrical coordinates for Z 11 Z √ 1y 2√ 1y 2 Z √ 4x 2y 2√ 4x 2y 2 xyz dz dxdy. 7. (10 Points) Section 7.1, Exercise 4(a) Evaluate the path integral of f ( x,y,z ) = x cos z along the path c : t 7→ t i + t 2 j ,t ∈ [0 , 1]. 8. (10 Points) Section 7.2, Exercise 2 Evaluate each of the following integrals: (a) Z c xdyy dx, c ( t ) = (cos t, sin t ) , ≤ t ≤ 2 π (b) Z c xdx + y dy, c ( t ) = (cos πt, sin πt ) , ≤ t ≤ 2 2 (c) Z c yz dx + xz dy + xy dz , where c consists of straightline segments joining (1 , , 0) to (0 , 1 , 0) to (0 , , 1) (d) Z c x 2 dxxy dy + dz , where c is the parabola z = x 2 ,y = 0 from (1 , , 1) to (1 , , 1) ....
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 Spring '08
 Ramakrishnan
 Math, Calculus, Linear Algebra, Algebra, Derivative, Rectangle, dx dy

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