5.3 The Fundamental Theorem of Calculus: Difference between revisions
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:1. FTC #1 <br> | :1. FTC #1 <br> | ||
: <math>\frac{d}{dx}\left[\int_{a(x)}^{b(x)}f(t)dt\right]=b'(x) | : <math>\frac{d}{dx}\left[\int_{a(x)}^{b(x)}f(t)dt\right]=b'(x)\cdotf(b(x))-a'(x)\cdotf(a(x))</math><br><br> | ||
:2. FTC #2 <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>. <math>F(x)</math> is called the <b>antiderivative</b> of <math>f(x)</math> <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>. <math>F(x)</math> is called the <b>antiderivative</b> of <math>f(x)</math> <br> | ||
Revision as of 17:53, 25 August 2022
Lecture[edit]
Lecture notes[edit]
- 1. FTC #1
- Failed to parse (unknown function "\cdotf"): {\displaystyle \frac{d}{dx}\left[\int_{a(x)}^{b(x)}f(t)dt\right]=b'(x)\cdotf(b(x))-a'(x)\cdotf(a(x))}
- 2. FTC #2
Where . is called the antiderivative of
![{\displaystyle {\frac {d}{dx}}\left[F(x)\right]=f(x)}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/3a5307d913d3c9aa3aa8e81954173adc0f657140)
Solutions[edit]
Mr. V solutions: 8, 20, 28
1 3 5 7 8 9 10 11 13 15 17 19 20 21 23 25 27 28 29 31 33 35 37 39 41 53