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Unformatted text preview: Math 32b Practice ﬁrst hour exam.
1. Sketch the region of integration, and then reverse the order of integration.
1
0 x f (x, y )dydx x2 2. Suppose that E is the ball of radius R and center at the origin and
f (x, y, z ) is a function deﬁned on E. Write the following as a multiple integral:
f (x, y, z )dV.
E 3. A thin plate covers the region bunded by the X axis and the lines
x = 1 and y = 2x. The density at (x, y ) is given by µ(x, y ) = 6x + 6u + 6.
Find the mass and center of gravity of the plate.
4. Calculate √ 1
−1 1 − x2 (x2 + y 2 )3/2 dydx. 0 2
2
5. Use the formula S = D fx + fy + 1dA to derive the formula for the
surface area of a sphere of radius R. 6. Suppose that the random variable (X, Y ) has probability distribution
f (x, y ) = C (x + y ) in the rectangle 0 ≤ x ≤ 1, 0 ≤ y ≤ 2, and it is zero
elsewhere.
a) Find the value of C.
b) Find the probability that (X, Y ) lies in the triangle above the diagonal
line from (0,0) to (1,2).
c) Find the X and Y mean values µ1 and µ2 . 1 ...
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This note was uploaded on 06/03/2011 for the course PHYSICS 1B 1b taught by Professor Corbin during the Winter '10 term at UCLA.
 Winter '10
 Corbin

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