Math22lO Quiz 9 (Section 13.1, 13.2, 13.3)
Name
Summer, 2012
Date
Dylan Zwick
7-o/
Instructions: Ple’se show all of your work as partial credit will be given where
appropriate, and there may be no credit given for problems where there is no work
shown. All answers should be completely simplified, unless otherwise stated.
1. (15 points) Take the region R((x,y):0x4,0y8) ,the function
+2xy—y+x and the partition P of R into eight equal squares by the
2
f(x,y)=x
3
linesx=2, y=2,y=4,andy=6.
,
Approximate
iT f(x,y)
f(Y) Ak
,
by calculating the corresponding Riemann sum
assuming that
(k,Yk)
are the centers of the eight squares.
3
K
L
Answer:
2. Evaluate the following integrals.
(J,i)
(
/5)
5
(7/7)
77
I
)
(a)
ff(x2+x+y2+1)dxdy .(lOpoints)
f’+
c3
31
f+
(+
-
*YLtI)
—
]dy
I)+yj= f1yLJy
*Lyt?Qy
(3)
yty3I
)
Answer:
2
1 2—x
(b)
ff
(x+y)dydx
(15 points)
—1 —x
J(z
-(x
y1)
UI
1
L
i’1
5
IO
ldJ
16
S
Answer:
)Jc
iI
x
L
5
tj(
vey
-
7-
j
-
+
75-
-
z_
Id