Tutorial
-2
()
dyd.
Evatuate
he
tegral
c)
4ydk.
3
d
3
d
c ) -
(+4)
d
+/,)
dx
+ ) -
(o+o
a+21
63
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Guidelines and tips
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Community
Ask the community
Ask the community for help and clear up your study doubts
University Rankings
Discover the best universities in your country according to Docsity users
Free resources
Our save-the-student-ebooks!
Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors
Mathematical Calculations Tutorial, Study notes of Mathematics
A tutorial on mathematical calculations involving integrals, curves, and polar coordinates. It includes several examples and exercises to evaluate integrals, find the area bounded by curves, and determine volumes. The tutorial also covers the conversion of coordinates from Cartesian to polar. suitable for students studying calculus and mathematical analysis.
Typology: Study notes
2021/2022
1 / 9
This page cannot be seen from the preview
Don't miss anything!
Related documents
Partial preview of the text
Download Mathematical Calculations Tutorial and more Study notes Mathematics in PDF only on Docsity!
Tutorial -
Evatuate he tegral ()^ dyd.
c) 4ydk.
3
d
d
c (^) ) (^) - (^) (+4) d
+/,) dx
- ) -(o+o
a+21 63
Evaluoae (^) the nteqTal y)chdy
C)oiyd
7
3
(1/
-)
30 +14^13210 IOS 3IS
bovnded by
Sketth he^ reaion^
R (^) in the^ y-plane^
bo0nded (^) b
The cuaves^ y^
and (^) y-x fnd^
tsaga. The
So
d
i -) d Y
A
ne u öm its
9-0 y
DO
y + sn y) dtdy
. 3ih^ y y
+y3sny 4y 4ysdydtt
sint dt
eFoo)
4+l6 y+16 Os
(^6 )
Cos
COs
( ,
Evaluae the nteario
ody by tcnvating polaa
coodio.
YSme
when
y
uDkan
dx-YiinOde
dy. YasO d e
from
drdy-YshoOro4o
Casinesine =
dr 4tosede
in=
Sune
dxdy (^) rteose rd#dE
d&
T COso)
LSte oto ) d
G4 (^) (sin'o coso)io lon- Cm--J0-0)-)]|
Sin eos"d
mm) mtH- --
tn-)
Cm-3)--
(1or [-) Cn--úu
mh)mth-2) --(1o1)
Evaua
cndex
)y
d
( Detevmine^
the volume^ the^ eqion^
bounded yth plane
3x+y+2i =^
that lies^ in^
he (^) t octant,
=
=12-yy -
--
ylimt ae
limits a -
2 0,^ i^6
volume (^) dydt
dyd
-2y-) dydr
6 d
S1-it - (^
-(| dt
72 12 86 +^1
-12/tf22) dt.
) de |.(3es
(L16+72 -H6)
T-M«S=/ hux),
Evaluae the^ voume^
Of he^ Sold^
i0 he^ rSt^
6ctant
bounded ky the^ planes^
x=0,
y=°,t:0,1+y+ Z=
s
ven +2y+t =
Z
to 6-z -.
O
Vgame da^ dydhu
c--2y
dy d