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JEE Main20231 Feb 2023Morning ShiftMathematicsDefinite IntegrationActual

If ∫ 0 1 x 21 + x 14 + x 7 2 x 14 + 3 x 7 + 6 1 / 7 d x = 1 l 11 m / n where l , m , n ∈ N , m and n are co-prime then l + m + n is equal to _____ .

Correct answer

0

Step-by-step solution

Let I = ∫ x 20 + x 13 + x 6 2 x 21 + 3 x 14 + 6 x 7 1 7 d x Put 2 x 21 + 3 x 14 + 6 x 7 = t ⇒ 42 x 20 + x 13 + x 6 d x = d t ∴ I = 1 42 ∫ 0 11 t 1 7 d t ⇒ I = 1 42 7 t 8 7 8 0 11 ⇒ I = 1 48 11 8 7 So, l = 48 ,   m = 8 , n = 7 ∴ l + m + n = 63

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