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  4. Let y=f(x) be a real-valued differentiable function on R (the set of all real numbers) such that f(1)=1. If f(x) satisfies x f prime(x)=x2+f(x)-2 then find the area enclosed by f(x) with x-axis between ordinates x =0 and x =3.

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Q. Let $y=f(x)$ be a real-valued differentiable function on $R$ (the set of all real numbers) such that $f(1)=1$. If $f(x)$ satisfies $x f^{\prime}(x)=x^2+f(x)-2$ then find the area enclosed by $f(x)$ with $x$-axis between ordinates $x =0$ and $x =3$.

Application of Integrals

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