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Question
If f'(x) = `x - 3/x^3`, f(1) = `11/2` find f(x)
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Solution
f'(x) = `x - 3/x^3`, f(1) = `11/2` .........[Given]
f(x) = `int"f'"(x) "d"x`
= `int(x - 3/x^3) "d"x`
= `int x "d"x - 3 int x^(-3) "d"x`
= `x^2/2 - 3 (x^(-2)/2) + "c"`
∴f(x) = `x^2/2 + 3/(2x^2) + "c"`
∴ f(1) = `(1)^2/2 + 3/(2(1)^2 + "c"`
∴ `11/2 = 1/2 + 3/2 + "c"`
∴ `11/2` =2 + c
∴ c = `7/2`
Substituting c = `7/2` in (i),, w get
f(x) = `x^2/2 + 3/(2x^2) + 7/2`
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