Question

If f'(x)=x-3/x^2 ,f(1)=11/2, find f(x)

Answer 1

Integrate once so that the derivative is cancelled.

So we have

f(x) =(x²/2)+(3/x)+k(Constt.of integration)

Given that f(1)=11/2

So 11/2=(1/2)+3+k

Or k=2

So f(x) =(x²/3)+(3/x)+2