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Question
If `f'(x) = x - (3)/x^3, f(1) = (11)/(2)`, find f(x)
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Solution
By the definition of integral,
f(x) = `int f'(x).dx`
= `int (x - 3/x^3).dx`
= `int x dx - 3 int x^-3 .dx`
= `x^2/(2) - (3x^((-2)))/((-2)) + c`
= `x^2/(2) + (3)/(2x^2) + c` ...(1)
f(1) = `(11)/(2)` ...(Given)
∴ `(1)/(2) + (3)/(2) + c = (11)/(2)`
∴ c = `(7)/(2)`
∴ f(x) = `x^2/(2) + (3)/(2x^2) + (7)/(2)` ...[By (1)]
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