jee-main 2025 Q16

jee-main · India · session1_28jan_shift1 Indefinite & Definite Integrals Finding a Function from an Integral Equation
Let for some function $\mathrm { y } = f ( x ) , \int _ { 0 } ^ { x } t f ( t ) d t = x ^ { 2 } f ( x ) , x > 0$ and $f ( 2 ) = 3$. Then $f ( 6 )$ is equal to
(1) 1
(2) 3
(3) 6
(4) 2
Let for some function $\mathrm { y } = f ( x ) , \int _ { 0 } ^ { x } t f ( t ) d t = x ^ { 2 } f ( x ) , x > 0$ and $f ( 2 ) = 3$. Then $f ( 6 )$ is equal to\\
(1) 1\\
(2) 3\\
(3) 6\\
(4) 2