Solve the problem.Find the center of mass of the region of constant density bounded by the paraboloid 
and the xy-plane.
A. 
= 0, 
= 0, 
= 27
B. 
= 0, 
= 0, 
= 3
C. 
= 0, 
= 0, 
= 
D. 
= 0, 
= 0, 
= 
Answer: A
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Solve the problem.Find a curve through the point 
whose length integral, 1 ? x ? 2, is 
A. y = 
x3
B. y = 3x3
C. y = 3x4
D. y = 
x4
Evaluate the integral by first performing long division on the integrand and then writing the proper fraction as a sum of partial fractions.
A. 2y2 - ln 
+ 4 ln 
+ C
B. 2y2 + ln 
+ ln 
+ C
C. 2y2 + ln 
+ (2y + 1) ln 
+ C
D. 2y2 + 4 ln 
+ ln 
+ C
Integrate the function.
dx
A. 
ln 
+ C
B. - 
ln 
+ C
C. 
ln 
+ C
D. - 
ln 
+ C
The graph of either a cubic or quartic polynomial f(x) with leading coefficient ±1 and integer zeros is shown. Write the complete factored form of f(x).
A. f(x) = (x + 4)(x - 1)(x - 2)(x + 4) B. f(x) = (x + 4)(x + 1)(x - 2)(x - 4) C. f(x) = (x + 4)(x - 1)(x + 2)(x - 4) D. f(x) = (x - 4)(x - 1)(x + 2)(x + 4)