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// TrigonometricIntegrals
https://www.math.ucdavis.edu/~kouba/CalcTwoDIRECTORY/trigintdirectory/TrigInt.html 1/7
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INTEGRATIONOFTRIGONOMETRICINTEGRALS
Recallthedefinitionsofthetrigonometricfunctions.
Thefollowingindefiniteintegralsinvolveallofthesewellknowntrigonometricfunctions.Someofthefollowingtrigonometryidentitiesmaybeneeded.
A.)
B.)
C.) sothat
D.) sothat
E.)
F.) sothat
G.) sothat
Itisassumedthatyouarefamiliarwiththefollowingrulesofdifferentiation.
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// TrigonometricIntegrals
https://www.math.ucdavis.edu/~kouba/CalcTwoDIRECTORY/trigintdirectory/TrigInt.html 2/7
Theseleaddirectlytothefollowingindefiniteintegrals.
1.)
2.)
3.)
4.)
5.)
6.)
Thenextfourindefiniteintegralsresultfromtrigidentitiesandusubstitution.
7.)
8.)
9.)
10.)
Wewillassumeknowledgeofthefollowingwellknown,basicindefiniteintegralformulas:
,where isaconstant
,where isaconstant
Mostofthefollowingproblemsareaverage.Afewarechallenging.Manyusethemethodofusubstitution.Makecarefulandpreciseuseofthedifferentialnotation and andbecarefulwhenarithmeticallyandalgebraicallysimplifyingexpressions.
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// TrigonometricIntegrals
https://www.math.ucdavis.edu/~kouba/CalcTwoDIRECTORY/trigintdirectory/TrigInt.html 3/7
PROBLEM1:Integrate .
ClickHEREtoseeadetailedsolutiontoproblem1.
PROBLEM2:Integrate .
ClickHEREtoseeadetailedsolutiontoproblem2.
PROBLEM3:Integrate .
ClickHEREtoseeadetailedsolutiontoproblem3.
PROBLEM4:Integrate .
ClickHEREtoseeadetailedsolutiontoproblem4.
PROBLEM5:Integrate .
ClickHEREtoseeadetailedsolutiontoproblem5.
PROBLEM6:Integrate .
ClickHEREtoseeadetailedsolutiontoproblem6.
PROBLEM7:Integrate .
ClickHEREtoseeadetailedsolutiontoproblem7.
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// TrigonometricIntegrals
https://www.math.ucdavis.edu/~kouba/CalcTwoDIRECTORY/trigintdirectory/TrigInt.html 4/7
PROBLEM8:Integrate .
ClickHEREtoseeadetailedsolutiontoproblem8.
PROBLEM9:Integrate .
ClickHEREtoseeadetailedsolutiontoproblem9.
PROBLEM10:Integrate .
ClickHEREtoseeadetailedsolutiontoproblem10.
PROBLEM11:Integrate .
ClickHEREtoseeadetailedsolutiontoproblem11.
PROBLEM12:Integrate .
ClickHEREtoseeadetailedsolutiontoproblem12.
PROBLEM13:Integrate
ClickHEREtoseeadetailedsolutiontoproblem13.
PROBLEM14:Integrate .
ClickHEREtoseeadetailedsolutiontoproblem14.
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// TrigonometricIntegrals
https://www.math.ucdavis.edu/~kouba/CalcTwoDIRECTORY/trigintdirectory/TrigInt.html 5/7
PROBLEM15:Integrate .
ClickHEREtoseeadetailedsolutiontoproblem15.
PROBLEM16:Integrate .
ClickHEREtoseeadetailedsolutiontoproblem16.
PROBLEM17:Integrate .
ClickHEREtoseeadetailedsolutiontoproblem17.
PROBLEM18:Integrate .
ClickHEREtoseeadetailedsolutiontoproblem18.
PROBLEM19:Integrate .
ClickHEREtoseeadetailedsolutiontoproblem19.
Someofthefollowingproblemsrequirethemethodofintegrationbyparts.Thatis,
.
PROBLEM20:Integrate .
ClickHEREtoseeadetailedsolutiontoproblem20.
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// TrigonometricIntegrals
https://www.math.ucdavis.edu/~kouba/CalcTwoDIRECTORY/trigintdirectory/TrigInt.html 6/7
PROBLEM21:Integrate .
ClickHEREtoseeadetailedsolutiontoproblem21.
PROBLEM22:Integrate .
ClickHEREtoseeadetailedsolutiontoproblem22.
PROBLEM23:Integrate .
ClickHEREtoseeadetailedsolutiontoproblem23.
PROBLEM24:Integrate .
ClickHEREtoseeadetailedsolutiontoproblem24.
PROBLEM25:Integrate .
ClickHEREtoseeadetailedsolutiontoproblem25.
PROBLEM26:Integrate .
ClickHEREtoseeadetailedsolutiontoproblem26.
PROBLEM27:Integrate .
ClickHEREtoseeadetailedsolutiontoproblem27.
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// TrigonometricIntegrals
https://www.math.ucdavis.edu/~kouba/CalcTwoDIRECTORY/trigintdirectory/TrigInt.html 7/7
ClickHEREtoreturntotheoriginallistofvarioustypesofcalculusproblems.
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