ax dx
cos
01
REMARK
where a s a constant
coss ax dx
1
11 4212
a
5
s ncan
s nlax
ax f e ther morn soddpos t ve nteger
s nm cos
s axtcostaf.IE scanax
the ntegral canbeeas lycomputedby subst tut on If n 2ktl KEZ
1 andrewr te
then usetheproperty dent ty s nk cos
11242 4 da
fs nmxles naxlkcosxdxandy. nt ateaab TfLubst tut on
C
s nsaxl
Ey
C
S
coaxax
cos
coax 2052 1
ax
Effy
C
cosu
AREAS OF PLANE REGIONS
IFFgfff .IE
ItetRbetheres onbetweeny
and y s x
A Ra Acre
ACR
a
reg onunder
a above x ax s
AIR
f x ax
AIR
reg onunders x above x ax s
where
Swat
Alka
4 s na.cz
tw
Aynı
EI
sen falan
11 s x forall
ab
s na.xdx. n
aya
areaoftheplane reg on Rbetweenthecurves y x 2x
4x
41 1 21
1112
AIR 9 squn ts
E
F ndtheareaoftheplanereg on ly ngtother ghtoftheparabola y 12
ne Y
d totheleft ofthe
s.ta sf.la
ntersect ons of
ya and ya12
E.TT
EIE.EE
IEIEEI
auf
fax tanx
343
ü
ğç
sec tanxdx
fsecaxtanaxsecxtanxd.FI
az az_1 da
sec
y ya12 ay
ns
se xdx
C tane tanja C
n
AIR
seen 1 ax
xdxy.jp
u
2
41212125 1212
sec
I
2
C
fsec4xdx
twoparabolas
2 2 2 7 ax
s nlax
1 tank sec
xtc AM
E
1 costal ax
_s nyal
tanax
F ndthe ntersect onpo ntsofthe
AIR
C
1 cos 2Nd
tankax
IEEE.EE
9
_yoga
gonna
E
4 2
sn
s n dx
sen f x DX
15
Sosaax s n
costanax
noter
dx
aga
c
wax
g max a
k ng
cosax
a un ts
sec
lu a da
C
Üç şey1 sextajdan
Yİ
C
a sen
s
2
Let represent theareaofthesamereg onas a def n te ntegral
termsof
AIR
da
F
1
UNH
F
reg on R
E F nd theareaoftheplane
2
between thecurves
y
2x and 9 4
soveatf f gsaw.fr
F
Fx
d ye
Ex
naw
IFE
a ax