If the integral Ι = ∫ e sin ⁡ x cos ⁡ x ⋅ x 2 + 2 x d x = e f x g x + C (where, C is the constant of integration), then the number of solution(s) of f x = g x is/are

Question

If the integral Ι = ∫ e sin ⁡ x cos ⁡ x ⋅ x 2 + 2 x d x = e f x g x + C (where, C is the constant of integration), then the number of solution(s) of f x = g x is/are, 0, 2, 4, 6

MARKS App · Accepted Answer

As, Ι = ∫ e f x f ′ x g x + g ′ x d x = e f x g x + C Thus, ∫ e sin ⁡ x cos ⁡ x ⋅ x 2 + 2 x d x = e sin ⁡ x ⋅ x 2 + C i.e. f x = sin ⁡ x & g x = x 2 Which intersect at ‘ 2 ’ points.

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