SecJEx3W01

# SecJEx3W01 - x 2 and x = y 2 7(SET UP DO NOT CALCULATE Find...

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Murat Atmaca Winter 2001 Math 22 Exam#3 1. Calculate the double integral Z 1 - 1 Z 2 x +1 sin( y 2 ) dy dx. 2. Calculate the triple integral Z 1 0 Z x 2 1 Z x + y 0 2 x 2 y dz dy dx. 3. Calculate the double integral Z Z R sin( x 2 + y 2 ) dA , where R is the disk of radius π centered at the origin . 4. (SET UP DO NOT CALCULATE) Find the Surface Area of the part of the plane 2 x + 3 y + 4 z = 12 bounded by the coordinates planes. 5. (SET UP DO NOT CALCULATE) Use the Cylindrical Coordinates to evaluate Z Z Z E ( x 3 + xy 2 ) dV , where E is the solid in the ﬁrst octant that lies beneath the paraboloid z = 1 - x 2 - y 2 . 6. Use a triple integral to ﬁnd the Volume of the solid under the paraboloid z = x 2 + y 2 and above the region bounded by the curves y =
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Unformatted text preview: x 2 and x = y 2 . 7. (SET UP DO NOT CALCULATE) Find the Center of the mass of the Lamina that D is bounded by the parabola y = 9-x 2 and x-axes if the density at each point ( x, y ) is the distance between ( x, y ) and y-axes. 8. Given the integral Z Z R x y dA where R is the region in the xy-plane bounded by the lines y =-2 x + 4 y =-2 x + 7 y = x-2 y = x + 1 . (a) Calculate the Jacobian of the transformation u = x-y and v = 2 x + y . (b) Sketch the uv-plane under transformation. (c) (SET UP DO NOT CALCULATE) the double integral Z Z R x y dA...
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