Let the domain of the function f(x)= log ₂ (log ₄ (log ₆(3+4x-x²))) be (a,b). If ∫₀^(a) x² dx = p - √(q) - √(r), with p,q,r and gcd (p,q,r)=1, where · is the greatest integer function, then p+q+r is equal to:

Integral Calculus: JEE Main 2025 Mathematics question

JEE Main 2025 · April, Unspecified (session-level dataset) · Q92

JEE Main 2025April, Unspecified (session-level dataset)MathematicsMediumIntegral Calculus369× since 2002

Let the domain of the function

f(x)=\log_2\bigl(\log_4\bigl(\log_6(3+4x-x^2)\bigr)\bigr)

(a,b)

. If

\displaystyle\int_0^a \lfloor x^2\rfloor\,dx = p - \sqrt{q} - \sqrt{r}

, with

p,q,r\in\mathbb{N}

and

\gcd(p,q,r)=1

, where

\lfloor\cdot\rfloor

is the greatest integer function, then

p+q+r

is equal to:

JEE Main 2025 Integral Calculus Question with Solution (April Unspecified (session-level dataset), Q92) | JEE Arc