SecFEx3W01

# SecFEx3W01 - M.Thomas Winter 2001 Math 22 1. Let f (x, y...

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M.Thomas Winter 2001 Math 22 Exam#3 1. Let f ( x, y )= x 2 + 16 y 2 and R= [1,5]x[0,1]. (a) Using the Midpoint Rule, ﬁnd a double Riemann sum with m=n=2 that estimates ZZ R f ( x, y ) dA . (b) Use your estimate of the volume to ﬁnd an estimate of the average value of f over R. 2. Evaluate the integral Z 0 1 Z y 1 1 1 - x 2 dxdy . 3. Find the moment of inertia about the y -axis for the lamina in the ﬁrst quadrant bounded by x = 0, y = 8, and y = x 3 if ρ ( x, y ) = e y 2 . 4. Set Up But Do Not Evaluate the multiple integral used to ﬁnd the volume of the solid which lies below the sphere x 2 + y 2 +( z - 3) 2 = 9 and above the xy -plane inside the cylinder x 2 + y 2 = 9. 5. Convert the integral Z - 4 4 Z 0 16
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## This note was uploaded on 01/24/2011 for the course MATH 22 taught by Professor Brigham during the Winter '08 term at Missouri S&T.

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