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Consider ∫ 3 x 4 + 2 x 2 + 1 x 4 + x 2 + 1 d x = f x . If f 1 = 3 , then f 2 2 is equal to

Correct answer

84

Step-by-step solution

Multiplying the numerator and denominator by x in the given integral, we get, f x = ∫ 3 x 5 + 2 x 3 + x x 6 + x 4 + x 2 d x Now substitute x 6 + x 4 + x 2 = t 2 ⇒ 2 3 x 5 + 2 x 3 + x d x = 2 t d t So, f x = ∫ t d t t = x 6 + x 4 + x 2 + C As f 1 = 3 ⇒ C = 0 Hence, f 2 = 64 + 16 + 4 ⇒ f 2 2 = 84

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