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
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

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