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If f^(prime)(x)=x-1/(x^2) and f(1)=1/2 ,...

If `f^(prime)(x)=x-1/(x^2)` and `f(1)=1/2` , find `f(x)` .

Text Solution

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`int f^{prime}(x) d x=int(x-frac{1}{x^{2}}) d x`
` We know int f^{prime}(x) d x=f(x) `
` Rightarrow f(x)=int(x-frac{1}{x^{2}}) d x `
` Rightarrow f(x)=int(x-x^{-2}) d x`
` Rightarrow f(x)=int x d x-int x^{-2} d x`
Recall` int x^{n} d x=frac{x^{n+1}}{n+1}+c`
` ...
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