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3 12 Tuo^ Cans^ a Laavelli^ along^ adacent^ nes^ he^ vebil,
Con A and ConB a V-{lt) ana V= at) he pecu'elg tt) (^) a (e) >0, o)^ -9(o)^.^ Find^ A
uncaons
te o ou tanta IKat^ Can^ A^ wil^ be^ ahead of^ Ca^ B^ al^
ma
t-b
kat Diatana^
travelaJ=|^
A Ne kooc^ Ca A
Can B = Jo b
eunu belweD hi dhot^ anao^ =^
6e)-4@)t
be lween
Tor
Finad Ke^ oua^ be^ luweeD^
y- Secc^ f^ Y-^ Sin^ ro
T/ Sec o = Sed =å
y=Set
y= Sin
Rqurd Area^ =^ Secr-^ Sinx)d*
= (^) Caux + Cbs^ x" =^ |^ +
3 Find^ z^ maa^ encdoseby^
-2-*# y=--x ()
CDo yo URSE L F) (^) above Find Ma^ asua^ in^ hz^ finst^ quadront^ bounde^ by^ Y=/R^ ard beloas by X-axis and ne J=X - 2 VR -2^ =^ +4x^ =>x-S+y^ =0^ =-10t-4)^ =o l=l o^ -,^ wALn^ =l,^ J=*1,^ "^ k^ 4s^ quaalrant^ = Ra PyoSa^ d (^) +-&)dt = g6+2x = s +2-
hi graphs -9 2 and y=x.
C/a)
Fn d Ki ahea^ betwen
(Do YoURSE L F) 6 Fin d ke ug^ ion^ enclosed^6 +*^ J=^3 rd Do oURSELF (8) Find Ae Cnc^ lose^ between Y^ *,^ y^ =^ aned^ k 2 x)d
) 2
/+ 2 Find aLa belweubelweeu^ J=x3^ y=3x-22^ belwe,^ = and = 2-
3x-2x -^ x^ x(3*-2-x)-O
3- 2 = X^ o^ x^ = O X-3x + 2.^ -0^ s^ X^ =o -)(a -2)^ =O^ 1=o 70,, 2 .'. aphs^ au^ (o.o),^ ()^ +^ (2,)). 3x2x=0^ X^ (3-2)^ =^ x=0 (^1)
Ka Area= x-Ta-2x)^ dk
-2T)- dd --+ +x *. (^). + -1 +1+
Fipd Uoluma 2
o a^ Spko 3= a
Sphe Can be Consiolere as (^) Suvolvinq ka (^) Semu (^2) Cicula igion
Ik circle
a noun X-aXiS ,a Volum = T 27 o')dx T x*)da
:Fin d Ihz^ Votums^ ellpsoid^
obt aina by en
X =I^ (a>b),^
anound
he elipse
axiS Do Yowrsek : One^ anch^ of^ ka^ Sm^ Cunve X-axis Find^ h^ Votame^ t^ k^ sslid^ 2ennue
-Sin is^ ne^ vowes^ oa
Votuma= y4 - Sin
JoT^ Sin'^ d
T (^) Jo Cos 2 2 d
2 G Find k Votume o k Soud geralkbvolvihg avolving (-x3(s)- between x =l ¢ X = 2
(^42) Sho hal a Voluma ef he Segmend Selus sph
haight
Deuce h Uolume a hemi 9phesu
ahd bane.^ a ali us a^ ,^ Th(30-).
Oun irca is^ x' y=a
-h 3
Uotume aS Saame nt
haighlh T d
a-h
Votu me = Ta^ )^ dx
a-h
-fa'- a-h
TTa a(a-h) +
T 24-a+ah^ +^ --3A+2a
h
-T+d'h + -ahtah
m|-a* -^
TA E-4= 4ThGa-
Nhen h^ = a^ , (^) weaet a^ hem^ sphe
Vatume Wa^ 2a^ a
