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}\int_{a(x)}^{b(x)}f(t)dt=b'(x)f(b(x))-a'(x)f(a(x))</math><br><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> | :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>\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> | ||
==Solutions== | |||
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]] | |||
![{\displaystyle {\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))}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/c6f2ad892079726c9f73d80191ed33deb30fc239)
![{\displaystyle {\frac {d}{dx}}\left[F(x)\right]=f(x)}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/3a5307d913d3c9aa3aa8e81954173adc0f657140)
