11 SENIOR HIGH SCHOOL
V V
BASIC CALCULUS VV
Quarter 4 – Module VV VV VV
8 Areas Between
VV VV V V
Curves V V
,Basic VCalculus V– VGrade
V11 VAlternative VDelivery
VMode
Quarter V4 V– VModule V8: VAreas VBetween
VCurves VFirst VEdition, V2020
Republic VAct V8293, Vsection V176 Vstates Vthat: VNo Vcopyright Vshall
Vsubsist Vin Vany Vwork Vof Vthe VGovernment Vof Vthe VPhilippines. VHowever, Vprior
Vapproval Vof Vthe Vgovernment Vagency Vor Voffice Vwherein Vthe Vwork Vis Vcreated
Vshall Vbe Vnecessary Vfor Vexploitation Vof Vsuch Vwork Vfor Vprofit. VSuch Vagency
Vor Voffice Vmay, Vamong Vother Vthings, Vimpose Vas Va Vcondition Vthe Vpayment
Vof Vroyalties.
Borrowed Vmaterials V(i.e., Vsongs, Vstories, Vpoems, Vpictures, Vphotos,
Vbrand Vnames, Vtrademarks, Vetc.) Vincluded Vin Vthis Vmodule Vare Vowned Vby
Vtheir Vrespective Vcopyright Vholders. VEvery Veffort Vhas Vbeen Vexerted Vto
Vlocate Vand Vseek Vpermission Vto Vuse Vthese Vmaterials Vfrom Vtheir Vrespective
Vcopyright Vowners. VThe Vpublisher Vand Vauthors Vdo Vnot Vrepresent Vnor Vclaim
Vownership Vover Vthem.
Published Vby Vthe VDepartment Vof
VEducation VSecretary: VLeonor VMagtolis
VBriones VUndersecretary: VDiosdado VM.
VSan VAntonio
Development Team of the Module
Writer: Gil S. Dael
Editor: Ronald G. Tolentino
Reviewer: Littie Beth S.
Bernadez Layout Artist:
Radhiya A. Ababon
Management Team: Senen Priscillo P. Paulin, CESO V Elisa L. Bagiuo,
EdD Joelyza M. Arcilla, EdD, CESE Rosela R. Abiera
Marcelo K. Palispis, JD, EdD Maricel S. Rasid
Nilita L. Ragay, EdD Elmar L. Cabrera
Printed Vin Vthe VPhilippines Vby V V
Department Vof VEducation V–Region VVII VSchools VDivision Vof VNegros VOriental
Office VAddress: Kagawasan, VAve., VDaro, VDumaguete VCity, VNegros
VOriental VTel V#: (035) V225 V2376 V/ V541 V1117
E-mail VAddress:
, 11
Basic Calculus
V
Quarter 4 – Module 8
V V V V
Areas Between
V V
Curves
V
V V
BASIC CALCULUS VV
Quarter 4 – Module VV VV VV
8 Areas Between
VV VV V V
Curves V V
,Basic VCalculus V– VGrade
V11 VAlternative VDelivery
VMode
Quarter V4 V– VModule V8: VAreas VBetween
VCurves VFirst VEdition, V2020
Republic VAct V8293, Vsection V176 Vstates Vthat: VNo Vcopyright Vshall
Vsubsist Vin Vany Vwork Vof Vthe VGovernment Vof Vthe VPhilippines. VHowever, Vprior
Vapproval Vof Vthe Vgovernment Vagency Vor Voffice Vwherein Vthe Vwork Vis Vcreated
Vshall Vbe Vnecessary Vfor Vexploitation Vof Vsuch Vwork Vfor Vprofit. VSuch Vagency
Vor Voffice Vmay, Vamong Vother Vthings, Vimpose Vas Va Vcondition Vthe Vpayment
Vof Vroyalties.
Borrowed Vmaterials V(i.e., Vsongs, Vstories, Vpoems, Vpictures, Vphotos,
Vbrand Vnames, Vtrademarks, Vetc.) Vincluded Vin Vthis Vmodule Vare Vowned Vby
Vtheir Vrespective Vcopyright Vholders. VEvery Veffort Vhas Vbeen Vexerted Vto
Vlocate Vand Vseek Vpermission Vto Vuse Vthese Vmaterials Vfrom Vtheir Vrespective
Vcopyright Vowners. VThe Vpublisher Vand Vauthors Vdo Vnot Vrepresent Vnor Vclaim
Vownership Vover Vthem.
Published Vby Vthe VDepartment Vof
VEducation VSecretary: VLeonor VMagtolis
VBriones VUndersecretary: VDiosdado VM.
VSan VAntonio
Development Team of the Module
Writer: Gil S. Dael
Editor: Ronald G. Tolentino
Reviewer: Littie Beth S.
Bernadez Layout Artist:
Radhiya A. Ababon
Management Team: Senen Priscillo P. Paulin, CESO V Elisa L. Bagiuo,
EdD Joelyza M. Arcilla, EdD, CESE Rosela R. Abiera
Marcelo K. Palispis, JD, EdD Maricel S. Rasid
Nilita L. Ragay, EdD Elmar L. Cabrera
Printed Vin Vthe VPhilippines Vby V V
Department Vof VEducation V–Region VVII VSchools VDivision Vof VNegros VOriental
Office VAddress: Kagawasan, VAve., VDaro, VDumaguete VCity, VNegros
VOriental VTel V#: (035) V225 V2376 V/ V541 V1117
E-mail VAddress:
, 11
Basic Calculus
V
Quarter 4 – Module 8
V V V V
Areas Between
V V
Curves
V
