25 FEB
2014 Math 101
Name:
Page 2
of
10 pages
Short Answer Questions. Each question is worth 3 points. Put a box around your
final answer, but NO CREDIT will be given for the answer without the correct accompanying
[24] L.
1,,-""r"", " I"*sin2s
o,=!4;: ';.ni-i:i
ca:czx'\drc
T.
E=
!= €silox) -+
(b)Evaruat"lffia2V
eoscZx)
k -L
+
t
Jx
&rcst;
G)
\ffi-
-J e-=K rtrt Czx)A'x
l'<* e = 4-r"'
Jr^= ^ 2xJx
f: [ -lzL.t -,
-it-
J
tJu
+a)\Lsi,^G)
^-*
+c
e=t (g,i Czx) -oosc4,)
{-C-
2014 Math 101
25 FEB
(c) Find the average value of
,t
|lz*e =
-69*;)
(d) Find
-['(*)
=
/'(r)
where
f (r)
:
cos cA
(
/(z) :
lo'*
J"
Page 3 of 10 pages
Name:
3e
sec2(r) dr over the interval [0,n la].
.J-xdx =
[r{61cos(r2) dr, where
'E -
hf b tA.
.4_ +c.^^
9+
-l:.
r > 0.
oo;(-t 'oc\)'
'l
e_
Furud cr'we',t*c'911'" t a''.t'L
-4 CaIu"JJt"J e.,,td f,^
cJrr";u^
^"tA)
25 FEB
2014 Math 101
Page 4 of 10 pages
Name:
+C
fdr
(e) Evaluate I .
.l rz-5117
L
7)
aAc+vr,\
\J3
/2-
\.t
s
dx-
Ic*-l':t
+
4
(.-tJ +C
( Ur" lano= 6 C^-V-\ '4 6r*',1*'*
oon 10- a^c;t"l,vtgad i^vnntd^-t"ru)
(f) A variable force of F(r) : kr newlons moves an object along a straight line when the
object is e metres from the origin. If the work done in moving the object from 1 metre
to 5 metres from the origin is 25 newton-metres, find the value of k.
2; W=
.J
?
J,
F*lJx=
4
F
Ydn=
!-&]ru
2
2
12'?o-=
=)
_-)
2t
=
4*'l=
z l,t
428_.
25 FEB
(g) Evaluat
2014 Math 101 Name:
"
Ir*
re-, d"r.
= /r nn I
J4
L>*L
'(
"-- \a
h*
[-e,e-q
L;ol] (
(h) Evaruat"
**
R->oo
Lal tl=x :) Jtt=Jr- I
= o** l- r.
Page 5 of 10 pages
I
+ !_
<
<.-LJ
X
J..r= e->cJx
[*e--J^J
\"
J4
J
(\
+ t- - a*\
jgg, (t . ;)' :
An v*e6ra!- 14,r* eas {A;' as a- Rt'
ls
{ f= *g'^*
o-,hK sqN^/L
7e_
\J v.'dx ginca Ars= += L
t1
4
e^lA
ck""'ltt
u-tdet 4"-A
ot a- P-"\t'th*' (
pincps
l1"lo . +(*
su/n i^
L4'
a4tB
,z) i^ n'eyuoL
'7tles Xi.t -- 4 -+ ,i=1,L,,..;
('*'Jr= tl'= e_L_trt
3 ll s s-13
J,(
YL.
25 FEB
2014 Math 101
Page 6 of 10 pages
Name:
1612. Find the area of the finite region .R bounded by the curves y
a : lrl.
:
tf2cos(trrl|)
and
-I n{errsac.t)'.r$* p".^"ts :
y
,If .*
=(x{
fT) =lr\
=) x=14
*-X='tret=fr)
X.
kno=
r4
('/x c*C,)-lxl)d*=
2lr@)--Jx
Jo
bA
U
=
fl
3,il' F a),n(SO _*1 o
W-L-A
lf ,E
\+-4
c*e%)=il'.{-'
14
j
-4
+in<<-
0
.f^,*rb{ *L** Ifu
-
a.oCt\,.
25 FEB
[6]
Bd+(
2074 Math 101
3. Find the function
-Fr+,
Wn 5o(,*
/ that satisfies f (r) :
{,(x)=
fA,JJr
Page 7 of 10 pages
Name:
be
n*
-
Io"
f ft) dt.
q ftx;.
@
bd s,.t".{tfu$,;r^,
[..t tr= +-+(^)
-'#= -4'&),
bt^^>t^
\.ar*,r,nts
O ,trt- -+dr
--)JA
dr
=) U.,k\= Le"
k
= t,('
>
<r,v\e
+ \'- k*l = Ce-"
-) {Cfl = !F- eA*,
'rnG +U
o'r'i^^^-A
\J,rrrt'. C? ?("8 >c = o
'pX"t^h\]*
#yl
F.o Ij *-rJt -e
=) 4 -(= O :) C-9.
l'l€^/...,
$co)=
{cx) = 4-\e-
-
25 FEB
[6]
2014 Math 101
Page 8 of 10 pages
Na,me:
andr:3
. Thetriangular
n:5.
region bounded by U:t,U:0,
Find the volume of the solid so generated.
is rotated about theline
5e+ {eil v+ a', a.w
\vr{"ga$.l^ t
6.
/-
\og
p cr-&)'-
\/=
r[*)1
o
=[r Cs- sye
- 9T r )3rrr
33
311c
778
- lTtr,
+Trd
e3
t
-Jo
JLTf
J.,
c
25 FEB
2014 Math 101
Page 9 of L0 pages
Name:
5. Find the volume of the solid generated by rotating the finite region bounded
:
Llr and 3o * 3y : 10 about the r-uris.
U
[6]
by
3r tl($)= 4e
t@9
v
7-fti
v=
(O
13 = (o:c
:) X-= k o{. )c:3
3>z
:l U=(9-x-,
-J3
ikr{"-n({d=.
a(l
sjar.r
84
25 FEB
2014 Math 101
Page 10 of 10 pages
Name:
[6] 6. A rectangular swimming pool 20 metres long and 8 metres wide has a sloping plane
bottom so that the depth of the pool is 1 metre at one end and 3 metres at the other end.
Find the total work that must be done to pump all the water in this pool when it is full over
the top edge of the pool.
__
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c,^/&J,\-sa <. wt
t+
&
.Aoy
io
s-: (U^,
t
_-d
5p(+ in*- $.o plac€
8wr
{n'
ra_
a=ft
l7''a dw,
=
,
Wr-=
l,ooo ka to^s-1J!DJ
j
ffi'
'20
_tl
(=
6{Paiu'dJ\eq&f"^,l{s.^&1{G
(oE.S
,6
C3^f)Jn
=
€x4.>6
s*(^n
C,*#tt
7
,,
qJ/\-e-o,
T,, @ dttb = 40oo
ooo .4"@gtT%
=-)
w=J:
JU
r-c-c{aJ;.qdd.!
z
o
>1 z-= 1O,p
,|.os,46.(e-f\dt
:y
Nu,..
\
x40( Nun
AU
+I^@L
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