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| FTC # 2- the <math>\frac{d}{dx}\left(\int\limits_{a(x)}^{b(x)}F(x)dx\right)</math> is F(b)-F(a) where F is the antiderivitive of f such that <math>F^\prime=f</math>
| | <math> |
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| 37) g(x)=<math>\int\limits_{1/2}^{\sqrt{3}/2}\frac{6}{\sqrt{1-t^2}} dt </math>
| | g(x)=\int\limits_{1/2}^{\sqrt{3}/2}\frac{6}{\sqrt{1-t^2}} dt |
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| <math>g^\prime(x)=\frac{d}{dx}\left(\int\limits_{1/2}^{\sqrt{3}/2}\frac{6}{\sqrt{1-t^2}} dt\right)=6sin^{-1}(x)\bigg|_{1/2}^{\sqrt{3}/2}</math>
| | g^\prime(x)=\frac{d}{dx}\left(\int\limits_{1/2}^{\sqrt{3}/2}\frac{6}{\sqrt{1-t^2}} dt\right)=6sin^{-1}(x)\bigg|_{1/2}^{\sqrt{3}/2} |
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| =<math>6sin^{-1}(\sqrt{3})/2)-(6sin^{-1}(1/2))</math> | | =6sin^{-1}(\sqrt{3})/2)-(6sin^{-1}(1/2)) |
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| =<math>\pi</math> | | =\pi |
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| [[5.3 The Fundamental Theorem of Calculus/1|1]]
| | </math> |
| [[5.3 The Fundamental Theorem of Calculus/3|3]]
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| [[5.3 The Fundamental Theorem of Calculus/5|5]]
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| [[5.3 The Fundamental Theorem of Calculus/7|7]]
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| [[5.3 The Fundamental Theorem of Calculus/8|8]]
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| [[5.3 The Fundamental Theorem of Calculus/9|9]]
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| [[5.3 The Fundamental Theorem of Calculus/10|10]]
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| [[5.3 The Fundamental Theorem of Calculus/11|11]]
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| [[5.3 The Fundamental Theorem of Calculus/13|13]]
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| [[5.3 The Fundamental Theorem of Calculus/15|15]]
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| [[5.3 The Fundamental Theorem of Calculus/17|17]]
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| [[5.3 The Fundamental Theorem of Calculus/19|19]]
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| [[5.3 The Fundamental Theorem of Calculus/20|20]]
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| [[5.3 The Fundamental Theorem of Calculus/21|21]]
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| [[5.3 The Fundamental Theorem of Calculus/23|23]]
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| [[5.3 The Fundamental Theorem of Calculus/25|25]]
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| [[5.3 The Fundamental Theorem of Calculus/27|27]]
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| [[5.3 The Fundamental Theorem of Calculus/28|28]]
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| [[5.3 The Fundamental Theorem of Calculus/29|29]]
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| [[5.3 The Fundamental Theorem of Calculus/31|31]]
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| [[5.3 The Fundamental Theorem of Calculus/33|33]]
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| [[5.3 The Fundamental Theorem of Calculus/35|35]]
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| [[5.3 The Fundamental Theorem of Calculus/37|37]]
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| [[5.3 The Fundamental Theorem of Calculus/39|39]]
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| [[5.3 The Fundamental Theorem of Calculus/41|41]]
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| [[5.3 The Fundamental Theorem of Calculus/53|53]]
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