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If the value of _ x 0 ( 1 x^5 ( ₀^x e^ -t^2 d t )- 1 x^4 + 1 3 x^2 ) is equal to m n (m, n are co-prime), find (m+n) .

Correct answer

11

Step-by-step solution

aligned & 1 3 _ x 0 3 ₀^x e^ -t^2 d t-3 x+x^3 x^5 ( 0 ) & = 1 3 _ x 0 3 e^ -x^2 -3+3 x^2 5 x^4 = 1 5 _ t 0 e^ -t -1+t t^2 = 1 10 aligned

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