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If f x is a quadratic polynomial with vertex V 1 , α , then the integral I = ∫ 0 2 e f x e f x + e f 2 - x d x is equal to

Correct answer

1

Step-by-step solution

As vertex is V 1 , α , thus the quadratic is symmetric about x = 1 ⇒ f 1 + x = f 1 - x Replacing x by x - 1 , we get, f x = f 2 - x Applying a + b - x in I and adding, we get, 2 I = ∫ 0 2 e f x + e f 2 - x e f x + e f 2 - x d x ⇒ 2 I = ∫ 0 2 1 d x = x 0 2 ⇒ 2 I = 2 - 0 ⇒ I = 1

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