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| FTC #1- <math>G(x)=f^\prime(x)</math> or in other words <math>\frac{d}{dx}\left[\int\limits_{a(x)}^{b(x)}F(x)dx\right]</math> is <math>\ b^\prime(x)*f(b(x))-a^\prime(x)*f(a(x))</math>
| | <math>g(x)=\int_{1-3x}^{1}\frac{u^3}{(1+u^2)} du</math> |
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| 17) <math>g(x)=\int\limits_{1-3x}^{1}\frac{u^3}{(1+u^2)} du</math>
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| <math>g\prime(x)=\frac{d}{dx}\left(\int\limits_{1-3x}^{1}\frac{u^3}{(1+u^2)} du\right) =(0)*f(1)-(-3)*f(1-3x)</math> | | <math>g\prime(x)=\frac{d}{dx}\left(\int\limits_{1-3x}^{1}\frac{u^3}{(1+u^2)} du\right) =(0)*f(1)-(-3)*f(1-3x)</math> |
Revision as of 20:21, 6 September 2022
which is equal to 
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or simplified to 
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