Let for some function $\mathrm{y}=\mathrm{f}(\mathrm{x}),{\int }_{0}^{\mathrm{x}}\mathrm{tf}(\mathrm{t})\mathrm{dt}={\mathrm{x}}^{2}\mathrm{f}(\mathrm{x}),$ $x0\text{ and }f(2)=3.$ Then $f(6)$ is equal to : [JEE Main 2025, 28 Jan (Shift 1)]

Question

Let for some function $\mathrm{y}=\mathrm{f}(\mathrm{x}),{\int }_{0}^{\mathrm{x}}\mathrm{tf}(\mathrm{t})\mathrm{dt}={\mathrm{x}}^{2}\mathrm{f}(\mathrm{x}),$ $x>0\text{ and }f(2)=3.$ Then $f(6)$ is equal to : [JEE Main 2025, 28 Jan (Shift 1)]

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Let for some function \(\mathrm{y}=\mathrm{f}(\mathrm{x}),{\int }_{0}^{\mathrm{x}}\mathrm{tf}(\mathrm{t})\mathrm{dt}={\m…

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