Question

The value of `int_(pi"/"4)^(pi"/"2)` cot θ cosec² θ dθ is ______.

Options

• `1/2`

• `-1/2`

• 0

• `-pi/8`

Answer 1

The value of `int_(pi"/"4)^(pi"/"2)` cot θ cosec² θ dθ is `underlinebb(1/2)`.

Explanation:

Since, `int_(pi"/"4)^(pi"/"2)` cot θ.cosec² θ dθ

Let cot θ = t

−cosec² θ dθ = dt

θ = `pi/4`, t = 1

θ = `pi/2`, t = 0

So, I = `int_1^0 t(-dt)`

I = `int_0^1 tdt`

= `[t^2/2]_0^1`

= `1/2`