Question

`int_6^(2/3) (dx)/(4 + 9x^2)` equals

पर्याय

• `pi/6`

• `pi/12`

• `pi/24`

• `pi/4`

Answer 1

`pi/24`

Explanation:

`int_0^(2/3) (dx)/(4 + 9x^2) = 1/9 int_0^(2/3) (dx)/(4/9 + x^2)`

= `1/9 - 1/(2/3) (tan^-1(x/(2/3)))_0^(2/3)`

= `1/6 [tan^-1  (3x)/2]_0^(2/3)`

= `1/6 [tan^-1 1 - tan^-1 0]`

= `1/6[pi/4 - 0]`

= `pi/24`