Let $\mathrm{f}(\mathrm{x})+2\mathrm{f}\left(\frac{1}{\mathrm{x}}\right)={\mathrm{x}}^{2}+5$ and $2g(x)-3g\left(\frac{1}{2}\right)=x,x0$. If $\alpha ={\int }_{1}^{2}f(x)dx$, and $\beta ={\int }_{1}^{2}g(x)dx$, then the value of $9\alpha +\beta$ is : [JEE Main 2025, 4 Apr (Shift 2)]

Question

Let $\mathrm{f}(\mathrm{x})+2\mathrm{f}\left(\frac{1}{\mathrm{x}}\right)={\mathrm{x}}^{2}+5$ and $2g(x)-3g\left(\frac{1}{2}\right)=x,x>0$. If $\alpha ={\int }_{1}^{2}f(x)dx$, and $\beta ={\int }_{1}^{2}g(x)dx$, then the value of $9\alpha +\beta$ is : [JEE Main 2025, 4 Apr (Shift 2)]

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Let \(\mathrm{f}(\mathrm{x})+2\mathrm{f}\left(\frac{1}{\mathrm{x}}\right)={\mathrm{x}}^{2}+5\) and \(2g(x)-3g\left(\frac…

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