Department
MathematicsCourse Code
MATH 2BProfessor
AllStudy Guide
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Section 7.2 -Trig Integrals
What are some easy examples of Trig Integrals?
●Example #1
○
() = () +
●Example #2
○
() = () +
Not so easy Trig Integrals
●Example #3
○
()
○How would we solve this?
○Convert () into something else
○
() =
()
()
■ Then use u-substitution
■ = (), = ()
■
○= ||+
○= (()) +
●Example #4
○
()
■ We can’t just convert this to
()
■ Instead, think about multiplying the by (1)
■
() 1
●What version of (1) should we use?
●
() () ()
() ()
●
() ()()
() ()
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■ Now we can use u-sub
● = () + (), = ()() + ()
■
●We can see that the u-subs fit perfectly
■ = (() + ()) +
●Remember to replace the u-subs
Now for slightly more difficult problems
●Example #5
○
()()
○ = (), = ()
○
()()()
■ We can rearrange our integral in a way that is already set up for us as
()
○
()(1 ())()
■ Using trig identity here; () + () = 1
■ Therefore, () = 1 ()
○
(1 )
■ Use u-sub
○
=
■ The rest is simplification
○
()
() +
■ Plug in = ()
●Example #6
○
()()
○
()()()
○
()(1 )()
■ = (), = ()
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