Question:

Apply King's Property: $2I = \pi \int_0^{\pi} \dfrac{\sin x}{1+\sin x} dx$. [1.5 Marks]
$2I = \pi \int_0^{\pi} \left( 1 - \dfrac{1-\sin x}{\cos^2 x} \right) dx = \pi \int_0^{\pi} (1 - \sec^2 x + \sec x \tan x) dx$. [1.5 Marks]
$= \pi [x - \tan x + \sec x]_0^{\pi} = \pi(\pi - 2)$. [1.5 Marks]
$I = \dfrac{\pi}{2}(\pi - 2)$. [0.5 Mark]

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🎯 Official CBSE Marking Scheme:
Applying King's Property to eliminate $x$: 1.5 Marks
Transforming integrand into integrable trigonometric forms: 1.5 Marks
Evaluating anti-derivatives at bounds: 1.5 Marks
Evaluating final definite integral $= (\pi/2)(\pi-2)$: 0.5 Mark