Let $\mathrm{f}(\mathrm{x})+2 \mathrm{f}\left(\frac{1}{\mathrm{x}}\right)=\mathrm{x}^2+5$ and $2 g(x)-3 g\left(\frac{1}{2}\right)=x, x0$. If $\alpha=\int_1^2 f(x) d x$, and $\beta=\int_1^2 g(x) d x$, 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 $2 g(x)-3 g\left(\frac{1}{2}\right)=x, x>0$. If $\alpha=\int_1^2 f(x) d x$, and $\beta=\int_1^2 g(x) d x$, then the value of $9 \alpha+\beta$ is: [JEE Main 2025, 4 Apr (Shift 2)]

YESPYQ · Accepted Answer

Options are free to see. Unlock the correct answer and full explanation with PYQ Pass.

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

Practice more JEE Maths PYQs