Mathematics

Find the antiderivative of f(x) given by $$f\left( x \right) =4{ x }^{ 3 }-\frac { 3 }{ { x }^{ 4 } } $$ such that f(2)=0


SOLUTION
$$ \rightarrow $$ let $$ f(x) = \int 4x^{3}-\frac{3}{x^{4}}dx$$
$$ = 4\left(\dfrac{x^{4}}{4}\right)-3\left(\dfrac{x^{-3}}{-3}\right)+C$$
$$ = x^{4}+\dfrac{1}{x^{3}}+C$$
Given $$ F(2) = 0 $$
$$ \Rightarrow 0 = 16+\dfrac{1}{8}+C$$
$$ \Rightarrow C = -\left(\dfrac{128+1}{8}\right) = \dfrac{-129}{8}$$
$$ \Rightarrow F(x) = x^{4}+\dfrac{1}{x^{3}}-\dfrac{129}{8}$$
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Subjective Medium Published on 17th 09, 2020
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