5.3 The Fundamental Theorem of Calculus: Difference between revisions

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


:1. FTC #1 <math>\int_{a(x))^(b(x))=</math><br>
:1. FTC #1 <br>
: <math>\frac{d}{dx}\left[\int_{a(x)}^{b(x)}f(t)\,dt\right]=b'(x)\cdot f(b(x))-a'(x)\cdot f(a(x))</math><br><br>
:2. FTC #2 <br>
: <math>\int_{a}^{b}f(x)\,dx=F(b)-F(a)</math><br> Where <math>\frac{d}{dx}\left[F(x)\right]=f(x)</math> and <math>F(x)</math> is called the <b>antiderivative</b> of <math>f(x)</math> <br>


: <math>x</math> is called the <b>input</b> or <b>argument</b> of the function and <math>f(x)</math> or <math>y</math> is called the <b>output</b> or <b>value</b> at <math>x</math>
==Solutions==
:: ex. If <math>f(x)=x^2+x+1</math> what is the value of <math>f</math> at <math>x=3</math>?
:: The value of <math>f</math> at <math>x=3 \text{ is } 13</math>


:2. <math>(x, y) \text{ or } (x, f(x)) </math> is called an <b>ordered pair</b> where <math>x</math> is the input and <math>y \text{ or } f(x)</math> is the output
Mr. V solutions: 8, 20, 28<br>
 
[[5.3 The Fundamental Theorem of Calculus/7|7]]
[[5.3 The Fundamental Theorem of Calculus/8|8]]
[[5.3 The Fundamental Theorem of Calculus/9|9]]
[[5.3 The Fundamental Theorem of Calculus/10|10]]
[[5.3 The Fundamental Theorem of Calculus/11|11]]
[[5.3 The Fundamental Theorem of Calculus/13|13]]
[[5.3 The Fundamental Theorem of Calculus/15|15]]
[[5.3 The Fundamental Theorem of Calculus/17|17]]
[[5.3 The Fundamental Theorem of Calculus/19|19]]
[[5.3 The Fundamental Theorem of Calculus/20|20]]
[[5.3 The Fundamental Theorem of Calculus/21|21]]
[[5.3 The Fundamental Theorem of Calculus/23|23]]
[[5.3 The Fundamental Theorem of Calculus/25|25]]
[[5.3 The Fundamental Theorem of Calculus/27|27]]
[[5.3 The Fundamental Theorem of Calculus/28|28]]
[[5.3 The Fundamental Theorem of Calculus/29|29]]
[[5.3 The Fundamental Theorem of Calculus/31|31]]
[[5.3 The Fundamental Theorem of Calculus/33|33]]
[[5.3 The Fundamental Theorem of Calculus/35|35]]
[[5.3 The Fundamental Theorem of Calculus/37|37]]
[[5.3 The Fundamental Theorem of Calculus/39|39]]
[[5.3 The Fundamental Theorem of Calculus/41|41]]
[[5.3 The Fundamental Theorem of Calculus/53|53]]
 
== Pending ==
[[5.3 The Fundamental Theorem of Calculus/1|1]]
[[5.3 The Fundamental Theorem of Calculus/3|3]]
[[5.3 The Fundamental Theorem of Calculus/5|5]]

Latest revision as of 16:22, 13 September 2022

Lecture[edit]

Lecture notes[edit]

1. FTC #1


2. FTC #2

Where and is called the antiderivative of

Solutions[edit]

Mr. V solutions: 8, 20, 28

7 8 9 10 11 13 15 17 19 20 21 23 25 27 28 29 31 33 35 37 39 41 53

Pending[edit]

1 3 5

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