Midterm1Review - MATH 32B MIDTERM 1 REVIEW PROBLEMS Problem...

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MATH 32B: MIDTERM 1 REVIEW PROBLEMS Problem 1. Find the average value of 2 x + y 2 over the triangle bounded by the lines y = x , y = 2 - x , and y = 0. Problem 2. Evaluate integraltext 1 0 integraltext 1 0 xye x 2 y dy dx . Problem 3. Find the volume of the solid cut off by the plane x + y + z = 1 in the first octant. Problem 4. Find the volume of the solid between the cone z = radicalbig x 2 + y 2 and the sphere x 2 + y 2 + z 2 = 1. Problem 5. Find the center of mass of a lamina in the first quadrant bounded by the curve y = 1 - x 2 with density function ρ ( x, y ) = 2 + x . Problem 6. Find the volume of the figure bounded above by the surface z = 2 + radicalbig x 2 + y 2 above the region in the plane inside of the circle with radius 2 and center at (0
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