Question

`int_(pi"/"11)^(9pi"/"22) (dx)/(1 + sqrttan x)` =

Options

• π/4

• π/22

• π/11

• 7π/44

Answer 1

7π/44

Explanation:

I = `int_(pi"/"11)^(9pi"/"22) (dx)/(1 + sqrttan x)`

I = `int_(pi"/"11)^(9pi"/"22) (sqrtcosx)/(sqrt(sin x) + sqrtcos x) dx`   ...(1)

= `int_(pi"/"11)^(9pi"/"22) (sqrt(cos ((9pi)/22 + pi/11 - x)))/(sqrt(sin((9pi)/22 + pi/11 - x)) + sqrt(cos((9pi)/22 + pi/11 - x)))`

I = `int_(pi"/"11)^(9pi"/"22) (sqrtcos)/(sqrt(sin x) + sqrt(cos x))`

Adding (i) and (ii)

2I = `(7pi)/22`

I = `(7pi)/44`