Definite IntegrationHard

Question

dx equals to :

Options

A.π/3
B.2π/3
C.π/6
D.none

Solution

Let x = 5 sin θ  ⇒ dx = 5 cos θ dθ
∴  I = . 5 cos θ dθ = dθ


Let I1 =       put cot θ = t
so  - cosec2 θ dθ = dt
i.e.    I1 = = √3
Let    I2 = = √3 -
so    I1 - I2 =

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