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Midterm

MATH 2B Midterm: MATH2B, Chapter 7.1 term test 2Premium


Department
Mathematics
Course Code
MATH 2B
Professor
All
Study Guide
Midterm

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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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