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The value of the integral Ι = ∫ 0 ∞ d x 1 + x 2020 1 + x 2 is equal to k π , then the value of 16 k is equal to

Correct answer

4

Step-by-step solution

Put t a n - 1 x = θ ⇒ x = tan ⁡ θ ⇒ d x = s e c 2 θ d θ ⇒ Ι = ∫ 0 π / 2 s e c 2 θ 1 + t a n 2020 θ s e c 2 θ d θ = ∫ 0 π 2 d θ 1 + t a n 2020 θ Ι = ∫ 0 π 2 c o s 2020 θ c o s 2020 θ + s i n 2020 θ d θ Applying a + b - x property and adding, we get, 2 Ι = ∫ 0 π 2 c o s 2020 θ + s i n 2020 θ c o s 2020 θ + s i n 2020 θ d θ ⇒ 2 Ι =

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