**Unformatted text preview: **(b) Write integral(s) in which you reverse the order of integration in (a). 5. [10 points] Consider the trapezoid with vertices (0 , 0) , (0 , w ) , (6 , w + 2), and (6 , 0). Given that the x-coordinate of the center of mass is 7 / 2, what is w ? Show your calculations; no credit for a guess. 6. [14 points] Consider a thin semicircular disk x 2 + y 2 ≤ 25 , y ≥ 0. (a) The disk has uniform density. Using polar coordinates ( r, θ ) write an expression, in terms of double integrals, that determines ¯ y , the y-coordinate of the center of mass of the semicircular disk. Calculate ¯ y . (b) Repeat (a) with disk density δ ( r, θ ) = r . 7. [14 points] A tetrahedron has vertices (0 , , 0), (1 , , 0), (0 , 2 , 0), and (0 , , 3). (a) Write a triple integral to calculate the volume of the tetrahedron. (b) Find the volume by evaluating this triple integral....

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- Fall '06
- PANTANO
- Math, Critical Point, Multivariable Calculus, semicircular disk