5.4 Indefinite Integrals and the Net Change Theorem: Difference between revisions

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==Lecture==
==Lecture==
* [ Link]


== Lecture notes ==
== Lecture notes ==


:1.
== Solutions ==
 
Mr. V solutions: 1, 6, 30<br>


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=== Block #1 ===
<math>\int\frac{x}{\sqrt{x^2+1}}dx=\sqrt{x^2+1}+c</math>
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<math>\frac{d}{dx}\left[(x^2+1)^\frac{1}{2}+c\right]= \frac{x}{\sqrt{x^2+1}}</math>
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let <math>a=x^2+1</math> and <math>b=a^{1/2}</math> then <math>\frac{da}{dx}=2x \text{ and } \frac{db}{da}=\frac{1}{2}a^{-1/2}</math>
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<math>\frac{da}{dx}\frac{db}{da} = 2x\frac{1}{2}a^{-1/2} = xa^{-1/2} = x(x^2+1)^{-1/2} = \frac{x}{\sqrt{x^2+1}}</math>
=== Pending ===


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Latest revision as of 17:59, 21 September 2022

Lecture[edit]

Lecture notes[edit]

Solutions[edit]

Mr. V solutions: 1, 6, 30

Block #1[edit]

1 3

Block #2[edit]

5 6 7 11 13 15 17

Block #3[edit]

21 23 25 27 29 30 31 33 35 37 39 41 43

Pending[edit]

9 31 35

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