1 Math 1432‐ Dr. Almus
Math 1432 DAY 13
Dr. Melahat Almus
If you email me, please mention the course (1432) in the subject line.
Bubble in PS ID and Popper Number very carefully. If you make a bubbling mistake, your scantron can’t be saved in the system. In that case, you will not get credit for the popper even if you turned it in.
Check your CASA account for Quiz due dates. Don’t miss any online quizzes!
Be considerate of others in class. Respect your friends and do not distract anyone during the lecture.
Chapter 8 - Techniques of Integration
Example: 2 1xxe dx
Example: xxe dx
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Section 8.1 - Integration by Parts
Let’s start with the product rule:
So, the integration by parts formula is:
We use it to “undo” the product rule.
udv uv vdu
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How do you know what to pick for u and for dv?
“Shortcut”: ILATE
Example 1: xxe dx
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Example 2: s inx x dx
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Example 3: 2 cosx x dx
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Example 4: 2 ln 5x x dx
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Example 5: cosxe x dx
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(*) Example 6: ln x dx
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Example 7: arctan x dx
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Exercise: arcsin x dx
Exercise: 2 arctanx x dx
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POPPER #
Question#
1
0
xxe dx
A) e B) 1 C) (e-1) D) (e+1) E) None of these
Question# ln xdx
A) ln( )x x C
B) 1
Cx
C) ln( )x x x C
D) ln( )x x x C
E) None of these