Answer is: option4
\( 1.571 \)Solution:
The curve is a four-leaved rose.
The area is determined by evaluating
\[ \int_{0}^{2\pi} \frac{1}{2}[r(\theta)]^2 \, d\theta = \int_{0}^{2\pi} \frac{1}{2}[\sin(2\theta)]^2 \, d\theta. \]
With a calculator, we determine the value of this definite integral to be approximately \( 1.571 \).
