Verified Solution • 2025–26 Session moderate

QJEEM25Maf8a7: JEE Main 2025 Mathematics - Class 12 JEEM25Maf8a7 Solution: Let . If the range of is , then equals :

Let f(x)=∫0xt(t2−9t+20)dt,1≤x≤5f(x)=\int\limits_0^x \mathrm{t}\left(\mathrm{t}^2-9 \mathrm{t}+20\right) \mathrm{dt}, 1 \leq x \leq 5 . If the range of ff is [α,β][\alpha, \beta] , then 4(α+β)4(\alpha+\beta) equals :

Multiple Choice Options

  • A 253
  • B 157
  • C 154
  • D 125

Step-by-Step Verified Solution

f′(x)=x3−9x2+20x=x(x−4)(x−5)f^{\prime}(x)=x^3-9 x^2+20 x=x(x-4)(x-5)

JEE Main 2025 (Online) 29th January Evening Shift Mathematics - Definite Integration Question 12 English Explanation

∴f(x)=x44−9x33+20x22f(1)=14−3+10=294=αf(4)=2564−3(64)|+10(16)=32=β4(α+β)=4(294+32)=157

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