Question

`int_0^{pi/2}((3sqrtsecx)/(3sqrtsecx + 3sqrt(cosecx)))dx` = ______ 

विकल्प

• `pi/2`

• `pi/3`

• `pi/4`

• `pi/6`

Answer 1

`int_0^{pi/2}((3sqrtsecx)/(3sqrtsecx + 3sqrt(cosecx)))dx` = `underline(pi/4)`.

Explanation:

 Let I = `int_0^{pi/2}((3sqrtsecx)/(3sqrtsecx + 3sqrt(cosecx)))dx` ............(i)

∴ I = `int_0^{pi/2} ((3sqrt(cosecx))/(3sqrt(cosecx) + 3sqrtsecx))`dx ................(ii) ............`[∵ int_0^a f(x)dx = int_0^a(a - x)dx]`

Adding (i) and (ii), we get

2I = `int_0^{pi/2} dx = [x]_0^{pi/2} = pi/2 ⇒ I = pi/4`