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Integral Calculus> if f ‘(x) = x – 1/x^2 and f(1) = ½ find f...

question mark

if f ‘(x) = x – 1/x^2 and f(1) = ½ find f(x)

taniska , 10 Years ago

Grade 12

1 Answers

Jitender Singh

Last Activity: 10 Years ago

Ans:
Hello Student,
Please find answer to your question

$f'(x) = x - \frac{1}{x^2}$
$\frac{df(x)}{dx} = x - \frac{1}{x^2}$
$df(x) = (x - \frac{1}{x^2})dx$
$\int df(x) = \int (x - \frac{1}{x^2})dx$
$f(x) = \frac{x^2}{2} + \frac{1}{x} + c$
$f(1) = \frac{1^2}{2} + \frac{1}{1} + c$
$\frac{1}{2} = \frac{1}{2} + 1 + c$
$c = -1$
$f(x) = \frac{x^2}{2} + \frac{1}{x} -1$

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