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The integral Ι = ∫ s i n x 2 + 2 x 2 c o s x 2 d x = x H x + C , (where C is the constant of integration). If the range of H ( x ) is a , b , then the value of a + 2 b is equal to

Correct answer

1

Step-by-step solution

Given integral Ι = ∫ 1 ⋅ s i n x 2 + x ⋅ 2 x c o s x 2 d x ∵ ∫ f ' g + f ⋅ g ' d x = ∫ f g ' d x = f ⋅ g + C = x ⋅ s i n x 2 + C ∴   H x = s i n x 2 , whose range is - 1,1 ∴   a = - 1 ,   b = 1 ⇒ a + 2 b = 1

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