Math 2210
Practice Final
Instructor: Mike Shrieve
Name:
The final is 2 hours. No calculators or equation sheets are allowed. Answer all questions.
These practice questions only cover what we have done since midterm 2. Please study the
first two practice midterms as well.
ZZ
(1) Evaluate
x + y dA, where S is the region in between y = x and y = x2 .
S
ZZ p
(2) Evaluate
4 − x2 − y 2 dA, where S is the region in the first quadrant bounded
S
by the circle x2 + y 2 = 4 and the lines y = 0 and y = x.
(3) Find the surface area of the part of the paraboloid z = x2 + y 2 that is cut off by the
plane z = 4.
Z
5
y
Z
Z
9
(4) Evaulate
xy dx dy dz.
0
0
z2
(5) Let F~ = cos x ı̂ + sin y ̂ + 3 k̂. Find div F~ and curl F~ .
Z
2x + 9z ds, where C is the curve given by x = t, y = t2 , z = t3 , 0 ≤ t ≤ 1.
(6) Evaluate
C
Z
(2,5)
(y 2 + 2xy) dx + (x2 + 2xy) dy.
(7) Evaulate
(0,0)
I
(8) Evaluate
C
F~ · ~n ds and
I
C
F~ · T~ ds where F~ = x ı̂ + y ̂ and C is the unit circle.