5.3 The Fundamental Theorem of Calculus/17

FTC #1

$G(x)=f^{\prime }(x)$ or in other words Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\frac {d}{dx}}} of Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \int \limits _{a(x)}^{b(x)}F(x)*dx} is Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \ b(x)*f(b(x))-a(x)*f(a(x))}

$y=\int \limits _{1-3x}^{1}{\frac {x^{3}}{(1+u^{2})}}dx$

so $y=\int \limits _{1-3x}^{1}{\frac {1}{(1+u^{2})}}x^{3},dx$

using the formula we get y=$(0)*f(1)-(-3)*f(1-3x)$ $(3)*f(1-3x)$

=$3*(1-3x)^{3}*{\frac {1}{(1+(1-3x)^{2})}}x^{3}+c$