参考案例文稿.pdf

APPLICATIONSOF

DEFINITEINTEGRALS

1.AverageFunctionValue

2.AreaBetweenCurves

3.VolumesofSolids

4.LengthsofneCurves,AreasofSurfaces

ofRevolution

5.Work,FluidPressureand

6.CentersofMass

AverageFunctionValue

Theaveragevalueofafunctionf(x)

overtheinterval[a,b]isgivenby,

1b

favgb−aaf(x)dx

AreaBetweenCurves

yyf(x)yyf

A

A

yf

oabxoabx

Af(x)dxA[f2(x)−f1(x)]dx

VolumesofSolids

MethodofSlicing

A(x)

oaxx+dxbx

VA(x)dx

VolumesofSolidsofRevolution/

DiskMethod

y

oxx+dxx

bb

VV

xy

VolumesofSolidsofRevolution/

WasherMethod

VR

xb(2

VolumesofSolidsofRevolution/

CylindricalSMethod

bssb

V2dx2xf(x)dx

yaradiusheighta



TheLengthofaCurve

y

A．Givencurveyf(x