Answer is: option4
\( \int_{0}^{\pi} (1 + \cos \theta)\, d\theta \)Solution:
In polar coordinates,
\[ \text{Area} = \frac{1}{2} \int_{0}^{2\pi} r^2 \, d\theta \]
\( r = \sqrt{1 + \cos \theta} \Rightarrow r^2 = 1 + \cos \theta \).
Using the symmetry of cosine,
\[ A = \frac{1}{2} \cdot 2 \int_{0}^{\pi} (1 + \cos \theta)\, d\theta = \int_{0}^{\pi} (1 + \cos \theta)\, d\theta. \]
