QJEEM21Ma0da6: JEE Main 2021 Mathematics - Class 12 JEEM21Ma0da6 Solution: If , x > 2, and (0) = 4, then (2) is __________.

Question

Verified Solution • 2025–26 Session moderate

If

x\phi (x) = \int\limits_5^x {(3{t^2} - 2\phi '(t))dt}

, x >

-

2, and

\phi

(0) = 4, then

\phi

(2) is __________.

Accepted Answer

x\phi (x) = \int\limits_5^x {3{t^2} - 2\phi '(t)dt}

x\phi (x) = {x^3} - 125 - 2[\phi (x) - \phi (5)]

x\phi (x) = {x^3} - 125 - 2\phi (x) - 2\phi (5)

\phi (0) = 4 \Rightarrow \phi (5) = {{133} \over 2}

\phi (x) = {{{x^3} + 8} \over {x + 2}}

\phi (2) = 4

Step-by-Step Verified Solution