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Most Important Selected Qs for JEE AdvancedMathematicsDefinite Integration

If _ -n ^n 3 x +1 3 x +1 d x=6 (4 e^2 ) , then find the value of n . [Note: k denotes the fractional part function of k .]

Correct answer

6

Step-by-step solution

aligned I_n & =2 n ₀^1 3 x +1 3 x +1 d x=2 n ( ₀^ 1 3 3 x+1 3 x+1 d x+ _ 1 3 ^ 2 3 3 x+1 3 x-1+1 d x+ _ 2 3 ^1 3 x+1 3 x-2+1 d x ) & =2 n ( 1 3 + 1 3 + 2 3 + _ 2 3 ^1 (1+ 2 3 x-1 ) d x )=2 n ( 1 3 + 1 3 + 2 3 + 1 3 + 2 3 ( (3 x-1))_ 2 3 ^1 ) & =2 n (1+ 2 3 + 2 2 3 )=2 n(1+ 2)=n (4 e^2 ) 6 (4 e^2 ) n & =6 aligned

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