Post on 05-Jul-2019
3213 Discussion Weeks
Volume of 3D regionProjection on my plane D
heightfunction EICX.gs EZE Zayz 224y
hexy i ZIYI Zi Xin
f Dp hex Nd'tdouble integral
yi Zuxyl
Compare with surface are
Sp hdr fab hirta at'andt
F 3D boundary carvescalar line integral
Changeof variables
Effigy3 Jacobian uh Ezn Ian.ie same
Changeof variables formulaG Do D fix y on D
p fixg dxjdf ffpofcxcuis.yeu.nl IYy dudV
dxdynl3Y'u1dudV areaofsmallpieces
Example polar coordinate
fit dodyerdrdd
r x
Nervally mo
ios rate
sino ruse f ri dxdynrdrdo
Sometimes weget µ u Fray insteadofnay _CHUN then
J.cat EiiTyl fYi.Yg It JcF5Similar for 3D Triple integral
WorkshutproblemsI
1
Eitiperez
i Dflx.pl xIyreYDo_Lino toerag
Heightfunction hcrf zr
p.itffphdAffp.hcr7rdrdp
changeof variablesdlt rdrdd
foudofoczr brdr
2n.f r3 fr831T
2 D LIExZyk4 lexyey xzayzoChange of variables Yn int n
Tf 11 21 45724 D g
dxdy Jdudv2 y7 Hgs Gcuv
i ffp Hy'dA ftp.xkyh zT dudv
tz1Do 2 3.3 I
3 Application to mechanics
qYSI rampdylidx 111111xuxgtzctx45fxdxy x
J.IE3 x0x7iExlodx
zHotIF Iz
4 Application to probabilityla p lxtfe 23 fodxffxpx.ycx.gldy
yaf e it dx
teat azeez q1 Itaz e At o
cb p qcz de acuate AZ
Eze at
TETHfothzpxeyczidzpnotherwaytudoit
fo Ee
itdz.isbydowbkhtegrd
fotozize
XZdtjodx.fi21T e Hdz
Zp