Math t82 - Collaboradve Activity - Review for Exam #1
Verify the general solution of the differentlal equation. Then find the particular solution
that satisfres the initial condition.
1. Solution
i y2 -9x2 - C
Differential equation
t
yy' -9x
-0
Initial Condition:
f(t)
=+
Set-up an integral that represents the area of the shaded region bounded by the graphs.
Do notevaluate.
3. !-x2,
2.
Je
+y=2, /n0
Sketctr the region bounded by the graphs of the algebraic frrnctions and find the area
of
the region.
4.x2-/*4,!=2x-l
5.
y -sinr, y =3sinx, x -0, x * trt
Find the volume of the sotid generated by revolving the reglon bounded by the graphs of
the equations about the given axis.
6. y
7.
y
=.[4,, ! =0, r =6 aboutthex-axis (usedisksorwashers)
j
-i.*, * -2, ! =0 aboutthey-axis (usedisksorwashers)
8. .y -
I
7, I
9. y *er,
n0, x *1,
)c
*2
aboutthey'axis (use cylindrical shells)
! *0, I =0, x =1 abouttheline x -4 (usemethodofyourchoice)
L0.y =x3, !
*8, r =0 abouttheline.y=9
(usemethodofyourchoice)
Find the arclength of the graph over the given interval.
1:L.
y
=5-2{7, lsx,s4
Find the area of the surdace generated by revolving the curve about they'axis.
12,
y*2x+5, lsxs4
fnqJ+1
t$f -
Colla.boraJr\p
Adu'\ -
Revieno
$.
Gxa6 #1
l.
,f-9^-=
c-
+'-qL'f
c-
=
f-rf=?
par}.t-trhr soh,r-tor
\b-1 : c
CrA
i
\r,fl-(t'&
a.
2
rl
I'cd-f +g +l)dl6,
I-,ia*
i
J?r--'l-(xL+)
<l
: J'I r-r\tx+a)dx
-l
dx
ri ,*ri(.i -("'i"'{
i
\-, []rri,
r3
-
ixt.
*t-
"
-q {.q +i -} -l +
Xr-.1 = ?X
-l
x'-J**tlrt;o
f'l"-g
.
o
(x-1lx+l);g
_61
-t-a
+,
nii-
\
"(3t'np - s;nx) dx
Jo
d^ =
: ltert*
Jo-- =
-XcosTT
-
rr
o
coox \
ro
- GZcotS
' , -ac-r) + lCr) -tr1
fo.(lil-ff
ax
a Itrr(x-z)dx
a
: rr[ ttr''{i
1x
va*
Lrl'f
b'
a-l
nA,
I' ,''
I
I
Jo
:
fr)'-
,
(? %)J dg,
S,1
j^+b1
"rr
Su{
[*g - hf]\.= [+t,l
TT
3 [Lta-4-]
=
E
: F**o' W*ffi*nu\dl:
E
fr"'-(f,)an
*arr[,ona-fiqry
-*
[n$';
,G
e.
U[=
r
jE r.,.ritlusr q6rmanb[
,.ir. (+-x\d
[
Jo,
t
dru-l'bt"-*-ttf fiw*:
ax =
a"
JiU- n#'
I
WAE*E(S:
<=5;' n[C+l -ta:Jd'6
["f +-u6$-cuf]
+
Doh,'r fvluttP,rg
1
"16
llr
I0.
0t*'
- y hf*,-,*^1*fo1 1l^
|'
rL+;-Tf+8oxJ
=
cYuPDU.!*g11stj5:
I%"(r-'yg)
d't
r
\ '- [ry
=
-, \
wt!!$s:
fftt(Q-*f,-
=
rT
-12+
l#* 8{-
.rL{r,' ;;i+"'lt-,+"]
\f . g
v.
=b^2x
"
-a^
| - t'('e\L =
u=
a'
Ji@"=
t2
C=l-wad U\.
Jro
L1
=
-I-- -
Q"t
a
t3+
21
\-
rral
I
.{_qx dlt
rl
fo
tJ')x
w,?2q
u=
lr9x
durQdX
t
du = dx
rr,,s,*
!*IN*
Lr-t
lpa=[0
la.
f'u
\
t?
-i*.*=,*
atr(
€)i
= Ii
5
2
r*
(*)'
ct
3
dy
ti.-')i
=$a--r)g =E"Llf 'l1f
1\
a
-- ,-
( T-.t)
,g
us,(
I;.F,.r
ao9rr=L
=
(,T-=)
'\
\
I
I
Qo
oA
!r^6,
I
G-au
4'x
I
:
Jtr
x = {lrrdx
,sn[l^,
/[
(z'
a.Rv
+
r-\
z-)
'tt
(, Y) =
a<rFrr
G):
lc.(3n