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 _____ .

Question

If &#8747; 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 , &#160; m , n &#8712; N , m and n are co-prime then l + m + n is equal to _____ .

Aicharya · Accepted Answer

Let I = &#8747; 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 &#8658; 42 x 20 + x 13 + x 6 d x = d t &#8756; I = 1 42 &#8747; 0 11 t 1 7 d t &#8658; I = 1 42 7 t 8 7 8 0 11 &#8658; I = 1 48 11 8 7 So, l = 48 , &#160; m = 8 , n = 7 &#8756; l + m + n = 63

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 ∈…

Solution

If &#8747; 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 , &#160; m , n &#8712;…

Solution

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 ∈…