log4log6(3+4x−x2)>0log6(3+4x−x2)>1
3+4x−x2>6x2−4x+3<0(x−1)(x−3)<0x∈(1,3) so a=1&b=3⇒∫02[x2]dx=?I=∫01[x2]dx+∫12[x2]dx+∫23[x2]dx+∫34[x2]dx=0+∣x∣12+2∣x∣23+3∣x∣34
=(2−1)+2(3−2)+3(2−3)=5−2−3⇒p+q+r=10
JEE Main 2025 — Mathematics Calculus
Let the domain of the function f(x)=log2log4log6(3+4x−x2) be (a, b). If ∫0b−a[x2]dx=p−q−r,p,q, r∈N,gcd(p,q,r)=1, where [⋅] is the greatest integer function, then p+q+r is equal to
Held on 3 Apr 2025 · Verified 6 Jul 2026.
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