1432 day13 inalmus/1432_day13_after.pdfd)xln()xxc e) none of these title microsoft word -...

1  Math 1432‐ Dr. Almus  

Math 1432 DAY 13

Dr. Melahat Almus

almus@math.uh.edu

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

2  Math 1432‐ Dr. Almus  

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