MAT1332A,FALL2014,Assignment 1

| August 14, 2017

MAT1332A,FALL2014,Assignment1DueFridaySeptember
19by3:00pm.
Lateassignmentswillnotbeaccepted;norwillunstapled
assignments.
Professorsinthemathdepartmentwillnotlendyouastapler;
donotaskforone.

Professor:Catalin
Rada

StudentName StudentNumber

Bysigningbelow,youdeclarethatthisworkwasyourownandthatyouhavenotcopiedfromanyotherindividualorothersource.

Signature

Question1.Findtheaveragevalueofthefunction
f(x)=

e2x
.png”>e2x+2013

overtheinterval
[0,1].

.png”>

Question2.Findtheindefiniteintegral
r

x3e?x2dx.

Usefirstasubstitution,thenuseintegration
byparts.
.png”>

Question3.Considerthedefiniteintegral
r0.5

?1

tan(x)dx.

.png”>FindthevalueofR6,theRiemannsumapproximationoftheintegralwith6subintervalsandfunctionevaluation
attherighthandendpointofeachsubinterval.

R6=

Question4.Sketchtheregionenclosed
bythecurvesy=12?x2andy=x2?6,andthenfinditsarea.

.png”>Don’tforgettoshowonyourregiontheintersectionpointsofthe2curves.

Answer:

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